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Thomas Aquinas: Commentary on Aristotle's Metaphysics: English 

COMMENTARY ON THE METAPHYSICS 

by 

Thomas Aquinas 

translated by John P. Rowan 
Chicago, 1961 

html-edited by Joseph Kenny, O.P. 

PROLOGUE 
THOMAS AQUINAS' OUTLINE OF THE BOOK 

Introduction (1-68) BOOK 1— 

The work itself (69-2663) 

What previous philosophers said about causes (69-272) 

Determination of the truth (273-2663) BOOK 2— 

With regard to universal truth (274-337) 

With regard to the truth about what belongs to this science (338-2663) BOOK 3 — 

Dialectical exposition of the problems (338-528) 

Demonstrative section 529-2663 BOOK 4 — 

List of things this science considers (529-748) 

Determination of these things (749-2663) BOOK 5— A 

The meanings of the terms used in this science (749-1 143) 

Names signifying causes (749-841) 

Names signifying the subject of this science (842-1032) 

Names signifying attributes or aspects of the subject (1033-1143) 

Determination of the realities this science considers (1 144-2663) BOOK 6 — 

The method of considering "being" in this science (1144-1244) 

The truth about "being" (1245-2663) BOOK 7— 

The truth about "being as being" (1245-2145) 
"Being" (1245-1919) 

As it is divided by the ten categories (1245-1767) 

The need to focus on substance (1245-1269) 

The truth about substance (1270-1767) 

The method and order of discussion (1270-1305) 

Sensible substances (1306-1767) 

General and logical considerations (1306-1680) 

Considering the principles of sensible substances (1681-1767) BOOK 8 — 

As it is divided by potency and act (1768-1919) BOOK 9— 

"One" and its concomitants (1920-2145) 


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Thomas Aquinas: Commentary on Aristotle's Metaphysics: English 

BOOK 
10— 

"One" in itself (1920-1982) 

In comparison with multitude (1983-2145) 

BOOK 

The first principles of being: separated substances (2146-2663) 
Preliminary considerations (2146-2415) 

BOOK 

Separated substances (2416-2663) ^ 


PROLOGUE 


When several things are ordained to one thing, one of them must rule or govern and the 
rest be ruled or governed, as the Philosopher, teaches in the Politics. This is evident in 
the union of soul and body, for the soul naturally commands and the body obeys. The 
same thing is true of the soul's powers, for the concupiscible and irascible appetites are 

ruled in a natural order by reason. Now all the sciences and arts are ordained to one 
thing, namely, to man's perfection, which is happiness. Hence one of these sciences and 
arts must be the mistress of all the others, and this rightly lays claim to the name 
wisdom; for it is the office of the wise man to direct others. 


We can discover which science this is and the sort of things with which it deals by 

carefully examining the qualities of a good ruler; for just as men of superior 
intelligence are naturally the rulers and masters of others, whereas those of great 
physical strength and little intelligence are naturally slaves, as the Philosopher says in 

the aforementioned book in a similar way that science which is intellectual in the 
highest degree should be naturally the ruler of the others. This science is the one which 

treats of the most intelligible objects. 

Now the phrase "most intelligible objects" can be understood in three ways. First, from 
the viewpoint of the order of knowing; for those things from which the intellect derives 
certitude seem to be more intelligible. Therefore, since the certitude of science is 
acquired by the intellect knowing causes, a knowledge of causes seems to be 
intellectual in the highest degree. Hence that science which considers first causes also 
seems to be the ruler of the others in the highest degree. 

Second, this phrase can be understood by comparing the intellect with the senses; for 
while sensory perception is a knowledge of particulars, the intellect seems to differ 
from sense by reason of the fact that it comprehends universals. Hence that science is 

pre-eminently intellectual which deals with the most universal principles. These 
principles are being and those things which naturally accompany being, such as unity 
and plurality, potency and act. Now such principles should not remain entirely 
undetermined, since without them complete knowledge of the principles which are 
proper to any genus or species cannot be had. Nor again should they be dealt with in 
any one particular science, for, since a knowledge of each class of beings stands in need 

if such principles, they would with equal reason be investigated in every particular 
science. It follows, then, that such principles should be treated by one common science, 
which, since it is intellectual in the highest degree, is the mistress of the others. 


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Third, this phrase can be understood from the viewpoint of the intellect's own 
knowledge. For since each thing has intellective power by virtue of being free from 
matter, those things must be intelligible in the highest degree which are altogether 
separate, from matter. For the intellect and the intelligible object must be proportionate 
to each other and must belong to the same genus, since the intellect and the intelligible 
object are one in act. Now those things are separate from matter in the highest degree 
which abstract not only from signate matter (as the natural forms taken universally of 
which the philosophy of nature treats) but from sensible matter altogether; and these are 
separate from matter not only in their intelligible constitution (ratio), as the objects of 

mathematics, but also in being (esse), as God and the intelligences. Therefore the 
science which considers such things seems to be the most intellectual and the ruler or 

mistress of the others. 

Now this threefold consideration should be assigned to one and the same science and 
not to different sciences, because the aforementioned separate substances are the 
universal and first causes of being. Moreover, it pertains to one and the same science to 
consider both the proper causes of some genus and the genus itself; for example, the 
philosophy of nature considers the principles of a natural body. Therefore, it must be 
the office of one and the same science to consider the separate substances and being in 
general (ens commune), which is the genus of which the aforementioned substances are 

the common and universal causes. 

From this it is evident that, although this science (metaphysics or first philosophy) 
studies the three things mentioned above, it does not investigate any one of them as its 

subject, but only being in general. For the subject of a science is the genus whose 
causes and properties we seek, and not the causes themselves of the particular genus 

studied; for a knowledge of the causes of some genus is the goal to which the 
investigation of a science attains. Now although the subject of this science is being in 
general, the whole of it is predicated of those things which are separate from matter 
both in their intelligible constitution and in being. For it is not only those things which 
can never exist in matter that are said to be separate from matter in their intelligible 
constitution and being, such as God and the intellectual substances, but also those 
which can exist without matter, as being in general. This could not be the case, 
however, if their being depended on matter. 

Therefore in accordance with the three things mentioned above from which this science 
derives its perfection, three names arise. It is called divine science or theology 
inasmuch as it considers the aforementioned substances. It is called metaphysics 
inasmuch as it considers being and the attributes which naturally accompany being (for 
things which transcend the physical order are discovered by the process of analysis, as 

the more common are discovered after the less common). And it is called first 
philosophy inasmuch as it considers the first causes of things. Therefore it is evident 
what the subject of this science is, and how it is related to the other sciences, and by 

what names it is designated. 


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Thomas Aquinas: Commentary on Aristotle's Metaphysics: English 


METAPHYSICS 
BOOK I 

ARISTOTLE'S INTRODUCTION 
HISTORY OF METAPHYSICAL INQUIRY 

CONTENTS 


LESSON 

1: 

LESSON 

2: 

LESSON 

3: 

LESSON 

4: 

LESSON 

5: 

LESSON 

6: 

LESSON 

7: 

LESSON 

8: 

LESSON 

9: 

LESSON 

10 

LESSON 

11 

LESSON 

12 

LESSON 

13 

LESSON 

14 

LESSON 

15 

LESSON 

16 

LESSON 

17 


The Dignity and Object of This Science 

Wisdom Considers Universal First Causes and First Principles 

The Nature and Goal of Metaphysics 

Opinions about the Material Cause 

Opinions about the Efficient Cause 

Love and Hate as Efficient Causes of Good and Evil 

The Views of the Atomists and the Pythagoreans 

The Pythagorean Doctrine about Contraries 

The Opinions of the Eleatics and Pythagoreans about the Causes of Things 

The Platonic Theory of Ideas 

A Summary of the Early Opinions about the Causes 

Criticism of the Views about the Number of Material Principles 

Criticism of the Pythagoreans' Opinions 

Arguments against the Platonic Ideas 

The Destruction of the Platonists' Arguments for Ideas 

Arguments against the View that Ideas Are Numbers 

Arguments against the View that the Ideas Are Principles of Being and 
Knowledge 


LESSON 1 

The Dignity and Object of This Science 
ARISTOTLE'S TEXT Chapter 1: 980a 21 -983a 3 

1. All men naturally desire to know. A sign of this is the delight we take in the senses; for 
apart from their usefulness they are loved for themselves, and most of all the sense which 
operates through the eyes. For not only that we may act, but even when we intend to do 
nothing, we prefer sight, as we may say, to all the other senses. The reason is that of all the 
senses this most enables us to know and reveals many differences between things. 

2. Animals by nature, then, are born with sensory power. 

3. Now in some animals memory arises from the senses, but in others it does not; and for this 
reason the former are prudent and more capable of being taught than those which are unable 


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to remember. Those which cannot hear sounds are prudent but unable to learn, as the bee and 
any other similar type of animal there may be. But any which have this sense together with 
memory are able to learn. 

4. Thus other animals live by imagination and memory and share little in experience, whereas 
the human race lives by art and reasoning. 

5. Now in men experience comes from memory, for many memories of the same thing 
produce the capacity of a single experience. And experience seems to be somewhat like 
science and art. 

6. But in men science and art come from experience; for "Experience causes art, and 
inexperience, luck," as Polus rightly states. Art comes into being when from many 
conceptions acquired by experience a Single universal judgment is formed about similar 
things. For to judge that this [medicine] has been beneficial to Callias and Socrates and many 
other individuals who suffer from this disease, is a matter of experience; but to judge that it 
has been beneficial to all individuals f a particular kind, as the phlegmatic, the bilious, or the 
feverish, taken as a lass, who suffer from this disease, is a matter of art. 

7. In practical matters, then, experience seems to differ in no way from art. ut we see that men 
of experience are more proficient than those who have theory without experience. The reason 
is that experience is a knowledge of in singulars, whereas art is a knowledge of universals. 
But all actions and processes of generation are concerned with singulars. For the physician 
heals man only incidentally, but he heals Socrates or Callias, or some individual that can be 
named, to whom the nature man happens to belong. Therefore, if anyone has the theory 
without experience, and knows the universal but not the singulars contained in this, he will 
very often make mistakes; for it is rather the individual man who is able to be cured. 

8. Yet we think that scientific knowledge and the ability to refute objections belong to art 
rather than to experience, and we are of the opinion that those who are proficient in art are 
wiser than men of experience, implying that it is more according to wisdom to know as one 
pursuing all things. 

9. Now this is because the former know the cause whereas the latter do not. For those who 
have experience know that something is so but do not know why, whereas the others know 
the why and the cause. For this reason, too, we think that the master planners in each art are to 
be held in greater esteem, and that they know more and are wiser than the manual laborers, 
because they understand the reasons for the things which are done. Indeed, we think that the 
latter resemble certain inanimate things, which act but do not know what they do, as fire 
burns. Therefore inanimate things perform each of their actions as a result of a certain natural 
disposition, whereas manual laborers perform theirs through habit, implying that some men 
are wiser not insofar as they are practical but insofar as they themselves have the theories and 
know the causes. 

10. In general a sign, of scientific knowledge is the ability to teach, and for this reason we 
think that art rather than experience is science. For those who have an art are able to teach, 
whereas the others are not. 

1 1 . Furthermore, we do not hold that any one of the senses is wisdom, since the cognition of 
singular things belongs especially to the senses. However, these do not tell us why a thing is 
so; for example, they do not tell us why fire is hot but only that it is so. 


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12 It is only fitting, then, that the one who discovered any art whatsoever that went beyond 
the common perceptions of men should be admired by men, not only because of some 
usefulness of his discoveries, but as one who is wise and as distinguishing [a thing] from 
others. And as more of the arts were discovered, some to supply the necessities of life, and 
others to introduce us [to the sciences] , those who discovered the former were always 
considered to be wiser than those who discovered the former, because their sciences were not 
for the sake of utility. Hence, after all such arts had already been developed, those sciences 
were discovered which are pursued neither for the sake of pleasure nor necessity. This 
happened first in those places where men had leisure. Hence the mathematical arts originated 
in Egypt, for there the priestly class was permitted leisure. The difference between art and 
science and similar mental states has been stated in our work on morals. 

13. Now the reason for undertaking this investigation is that all men think that the science 
which is called wisdom deals with the primary causes and principles of things. Hence, as we 
have said before (8, 9), the man of experience is considered to be wiser than one who has any 
of the senses; the artist wiser than the man of experience; the master planner wiser than the 
manual laborer and speculative knowledge wiser than practical knowledge. It is quite evident 
then, that wisdom is a science of certain causes and principles. 

COMMENTARY 

Three reasons why people naturally desire to know 

1. Aristotle first sets down an introduction to this science, in which he treats of two things. 
First (2), he points out with what this science is concerned. Second (53), he explains what 
kind of science it is ("That this is not a practical science"). 

In regard to the first he does two things. First, he shows that the office of this science, which 
is called wisdom, is to consider the causes of things. Second (36), he explains with what 
causes or kinds of causes it is concerned ("But since we are in search"). 

In regard to the first he prefaces certain preliminary considerations form which he argues in 
support of his thesis. Second (35), he draws a conclusion from these considerations ("Now the 
reason for undertaking"). 

In regard to the first he does two things. First, he makes clear the dignity of scientific 
knowledge in general. Second (9), he explains the hierarchy in knowing ("Animals by 
nature"). 

Now he establishes the dignity of scientific knowledge from the fact that it is naturally 
desired as an end by all men. Hence, in regard to this he does two things. First, he states what 
he intends [to prove]. Second (1), he proves it ("A sign of this"). 

Accordingly, he says, first, that the desire to know belongs by nature to all men. 

2. Three reasons can be given for this: 

The first is that each thing naturally desires its own perfection. Hence matter is also said to 
desire form as any imperfect thing desires its perfection. Therefore, since the intellect, by 
which man is what he is, considered in itself is all things potentially, and becomes them 
actually only through knowledge, because the intellect is none of the things that exist before it 


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understands them, as is stated in Book III of The Soul, so each man naturally desires 
knowledge just as matter desires form. 

3. The second reason is that each thing has a natural inclination to perform its proper 
operation, as something hot is naturally inclined to heat, and something heavy to be moved 
downwards. Now the proper operation of man as man is to understand, for by reason of this 
he differs from all other things. Hence the desire of man is naturally inclined to understand, 
and therefore to possess scientific knowledge. 

4. The third reason is that it is desirable for each thing to be united to its source, since it is in 
this that the perfection of each thing consists. This is also the reason why circular motion is 
the most perfect motion, as is proved in Book VIII of the Physics, because its terminus is 
united to its starting-point. Now it is only by means of his intellect that man is united to the 
separate substances, which are the source of the human intellect and that to which the human 
intellect is related as something imperfect to something perfect. It is for this reason, too, that 
the ultimate happiness of man consists in this union. Therefore man naturally desires to know. 
The fact that some men do not devote any study to this science does not disprove this thesis; 
for those who desire some end are often prevented from pursuing it for some reason or other, 
either because of the difficulty of attaining it, or because of other occupations. And in this 
way, too, even though all men desire knowledge, still not all devote themselves to the pursuit 
of it because they are held back by other things, either by pleasures or the needs of the present 
life; or they may even avoid the effort that learning demands because they are lazy. Now 
Aristotle makes this statement in order to show that it is not pointless to search for a science 
that is not useful for anything else, as happens in the case of this science, since a natural 
desire cannot exist in vain. 

5. Then he establishes his thesis by means of an example. Since our senses serve us in two 
respects: in knowing things and in meeting the needs of life, we love them for themselves 
inasmuch as they enable us to know and also assist us to live. This is evident from the fact 
that all men take the greatest delight in that sense which, is most knowing, i.e., the sense of 
sight, which we value not merely in order to do something, but even when we are not required 
to act at all. The reason is that this sense — that of sight — is the most knowing of all our senses 
and makes us aware of many differences between things. 

6. In this part it is clear that he gives two reasons why sight is superior to the other senses in 
knowing. The first is that it knows in a more perfect way; and this belongs to it because it is 
the most spiritual of all the senses. For the more immaterial a power is, the more perfectly it 
knows. And evidently sight is a more immaterial sense, if we consider the modification 
produced in it by its object. For all other sensible objects change both the organ and medium 
of a sense by a material modification, for example, the object of touch by heating and cooling, 
the object of taste by affecting the organ of taste with some flavor through the medium of 
saliva, the object of hearing by means of motion in the body, and the object of smell by means 
of the evaporation of volatile elements. But the object of sight changes the organ and medium 
of sight only by a spiritual modification; because neither the pupil of the eye nor the air 
becomes colored, but these only receive the form of color in a spiritual mode of being. 
Therefore, because actual sensation consists in the actual modification of a sense by its object, 
it is evident that that sense which is changed in a more immaterial and spiritual way is more 
spiritual in its operation. Hence sight judges about sensible objects in a more certain and 
perfect way than the other senses do. 


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7. The other reason which he gives for the superiority of sight is that it gives us more 
information about things. This is attributable to the nature of its object, for touch and taste, 
and likewise smell and hearing, perceive those accidents by which lower bodies are 
distinguished from higher ones. But sight perceives those accidents which lower bodies have 
in common with higher ones. For a thing is actually visible by means of light, which is 
common both to lower and higher bodies, as is said in Book II of The Soul. Hence the 
celestial bodies are perceptible only by means of sight. 

8. There is also another reason. Sight informs us of many differences between things, for we 
seem to know sensible things best by means of sight and touch, but especially by means of 
sight. The reason for this can be drawn from the fact that the other three senses perceive those 
accidents which in a way flow from a sensible body and do not remain in it. Thus sound 
comes from a sensible body inasmuch as it flows away from it and does not remain in it. The 
same thing is true of the evaporation of volatile elements, with which and by which odor is 
diffused. But sight and touch perceive those accidents which remain in sensible bodies, such 
as color, warmth and coldness. Hence the judgment of sight and touch is extended to things 
themselves, whereas the judgment of hearing and smell is extended to those accidents which 
flow from things and not to things themselves. It is for this reason that figure and size and the 
like, by which a sensible being itself is disposed, are perceived more by sight and touch than 
by the other senses. And they are perceived more by sight than by touch, both because sight 
knows more efficaciously, as has been pointed out (C 6), and also because quantity and those 
[accidents] which naturally follow from it, which are seen to be the common sensibles, are 
more closely related to the object of sight than to that of touch. This is clear from the fact that 
the object of sight belongs in some degree to every body having some quantity, whereas the 
object of touch does not. 

9. Animals by nature, then (2). 

Here he considers the hierarchy in knowledge. He does this, first (9), with respect to brute 
animals; and, then (14), with respect to men ("Thus other animals"). 

With respect to brute animals he mentions first what all animals have in common; and second 
(10), that by which they differ and surpass one another ("Now in some animals"). 

Now all animals are alike in the respect that they possess by nature the power of sensation. 
For an animal is an animal by reason of the fact that it has a sentient soul, which is the nature 
of an animal in the sense in which the distinctive form of each thing is its nature. But even 
though all animals are naturally endowed with sensory power, not all animals have all the 
senses, but only perfect animals. All have the sense of touch, for this sense in a way is the 
basis of all the other senses. However, not all have the sense of sight, because this sense 
knows in a more perfect way than all the other senses. But touch is more necessary; for it 
perceives the elements of which an animal is composed, namely, the hot, cold, moist and dry. 
Hence, just as sight knows in a more perfect way than the other senses, in a similar way touch 
is more necessary inasmuch as it is the first to exist in the process of generation. For those 
things which are more perfect according to this process come later in the development of the 
individual which is moved from a state of imperfection to one of perfection. 

10. Now in some animals (3). 

Here he indicates the different kinds and three levels of knowing found among brute animals. 
For there are certain animals which have sensation, although they do not have memory which 


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comes from sensation. For memory accompanies imagination, which is a movement caused 
by the senses in their act of sensing, as we find in Book II of The Soul. But in some animals 
imagination does not accompany sensation, and therefore memory cannot exist in them. This 
is found verified in imperfect animals which are incapable of local motion, such as shellfish. 
For since sensory cognition enables animals to make provision for the necessities of life and 
to perform their characteristic operations, then those animals which move towards something 
at a distance by means of local motion must have memory. For if the anticipated goal by 
which they are induced to move did not remain in them through memory, they could not 
continue to move toward the intended goal which they pursue. But in the case of immobile 
animals the reception of a present sensible quality is sufficient for them to perform their 
characteristic operations, since they do not move toward anything at a distance. Hence these 
animals have an indefinite movement as a result of confused [or indeterminate] imagination 
alone, as he points out in Book III of The Soul. 

1 1 . Again, from the fact that some animals have memory and some do not, it follows that 
some are prudent and some not. For, since prudence makes provision for the future from 
memory of the past (and this is the reason why Tully in his Rhetoric, Book II, makes memory, 
understanding and foresight parts of prudence), prudence cannot be had by those animals 
which lack memory. Now those animals which have memory can have some prudence, 
although prudence has one meaning in the case of brute animals and another in the case of 
man. Men are prudent inasmuch as they deliberate rationally about what they ought to do. 
Hence it is saidin Book VI of the Ethics, that prudence is a rationally regulated plan of things 
to be done. But the judgment about things to be done which is not a result of any rational 
deliberation but of some natural instinct is called prudence in other animals. Hence in other 
animals prudence is a natural estimate about the pursuit of what is fitting and the avoidance of 
what is harmful, as a lamb follows its mother and runs away from a wolf . 

12. But among those animals which have memory some have hearing and some do not. And 
all those which cannot hear (as the bee or any other similar type of animal that may exist), 
even though they have prudence, are still incapable of being taught, i.e., in the sense that they 
can be habituated to the doing or avoiding of something through someone else's instruction, 
because such instruction is received chiefly by means of hearing. Hence in The Senses and 
Their Objects it is stated that hearing is the sense by which we receive instruction. 
Furthermore, the statement that bees do not have hearing is not opposed in any way to the 
observation that they are frightened by certain sounds. For just as a very loud sound kills an 
animal and splits wood, as is evident in the case of thunder, not because of the sound but 
because of the violent motion of the air in which the sound is present, in a similar fashion 
those animals which lack hearing can be frightened by the sounding air even though they 
have no perception of sound. However, those animals which have both memory and hearing 
can be both prudent and teachable. 

13. It is evident, then, that there are three levels of knowing in animals. The first level is that 
had by animals which have neither hearing nor memory, and which are therefore neither 
capable of being taught nor of being prudent. The second level is that of animals which have 
memory but are unable to hear, and which are therefore prudent but incapable of being taught. 
The third level is that of animals which have both of these faculties, and which are therefore 
prudent and capable of being taught. Moreover, there cannot be a fourth level, so that there 
would be an animal which had hearing but lacked memory. For those senses which perceive 
their sensible objects by means of an external medium — and hearing is one of these — are 
found only in animals which have locomotion and which cannot do without memory, as has 
been pointed out (10). 


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14. Thus other animals (4). 

Here he explains the levels of human knowing; and in regard to this he does two things. First 
(14), he explains how human knowing surpasses the knowing of the abovementioned animals. 
Second (17), he shows how human knowing is divided into different levels ("Now in men"). 

Accordingly, in the first part (4) he says that the life of animals is ruled by imagination and 
memory: by imagination in the case of imperfect animals, and by memory in the case of 
perfect animals. For even though the latter also have imagination, still each thing is said to be 
ruled by that [power] which holds the highest place within it. Now in this discussion life does 
not mean the being of a living thing, as it is understood in Book II of The Soul, when he says 
that "for living things to live is to be"; for the life of an animal in this sense is not a result of 
memory or imagination but is prior to both of these. But life is taken to mean vital activity, 
just as we are also accustomed to speak of association as the life of men. But by the fact that 
he establishes the truth about the cognition of animals with reference to the management of 
life, we are given to understand that knowing belongs to these animals, not for the sake of 
knowing, but because of the need for action. 

15. Now, as is stated below (18), in men the next thing above memory is experience, which 
some animals have only to a small degree. For an experience arises from the association of 
many singular [intentions] received in memory. And this kind of association is proper to man, 
and pertains to the cogitative power (also called particular reason), which associates particular 
intentions just as universal reason associates universal ones. Now since animals are 
accustomed to pursue or avoid certain things as a result of many sensations and memory, for 
this reason they seem to share something of experience, even though it be slight. But above 
experience, which belongs to particular reason, men have as their chief power a universal 
reason by means of which they live. 

16. And just as experience is related to particular reason [in men], and customary activity to 
memory in animals, in a similar way art is related to universal reason. Therefore, just as the 
life of animals is ruled in a perfect way by memory together with activity that has become 
habitual through training, or in any other way whatsoever, in a similar way man is ruled 
perfectly by reason perfected by art. Some men, however, are ruled by reason without art; but 
this rule is imperfect. 

17. Now in men (5). 

Here he explains the different levels of human knowing; and in regard to this he does two 
things. First (17), he compares art with experience; and, second (31), he compares speculative 
art with practical art ("It is only fitting"). 

He treats the first point in two ways. First, he explains how art and experience originate. 
Second (20), he explains how one is superior to the other ("In practical matters"). 

In regard to the first he does two things. First, he explains how each of the above originates. 
Second (18), he makes this clear by means of an example ("For to judge"). 

In regard to the first he does two things. First, he describes how experience originates, and 
second (18), how art originates ("But in men, science"). 


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He says first (5), then, that in men experience is caused by memory. The way in which it is 
caused is this: from several memories of a single thing a man acquires experience about some 
matter, and by means of this experience he is able to act easily and correctly. Therefore, 
because experience provides us with the ability to act easily and correctly, it seems to be 
almost the same as science and art. For they are alike inasmuch as in either case from many 
instances a single view of a thing is obtained. But they differ inasmuch as universals are 
grasped by art and singular things by experience, as is stated later (18). 

18. But in men science and art (6). Here he describes the way in which art arises. He says that 
in men science and art come from experience, and he proves this on the authority of Polus, 
whp says that "Experience causes art and inexperience luck." For when an inexperienced 
person acts correctly, this happens by chance. Furthermore, the way in which art arises from 
experience is the same as the way spoken of above in which experience arises from memory. 
For just as one experiential cognition comes from many memories of a thing, so does one 
universal judgment abour all similar things come from the apprehension of many experiences. 
Hence art has this [unified view] more than experience, because experience is concerned only 
with singulars, whereas art has to do with universals. 

19. Thereupon he makes this clear by means of examples ("But in men"). For when a man has 
learned that this medicine has been beneficial to Socrates and Plato, and to many other 
individuals who were suffering from some particular disease, whatever it may be, this is a 
matter of experience; but when a man learns that this particular treatment is beneficial to A 
men who have some particular kind of disease and some particular kind of physical 
constitution, as it has benefited the feverish, both the phlegmatic and the bilious, this is now a 
matter of art. 

20. In practical matters (7). 

He compares art to experience from the viewpoint of pre-eminence; and in regard to this he 
does two things. First (20), he compares them from the viewpoint of action; and, second (23), 
from the viewpoint of knowledge ("Yet we think"). 

He says then that in practical matters experience seems to differ in no way from art; for when 
it comes to acting, the difference between experience and art, which is a difference between 
the universal and the singular, disappears, because art operates with reference to singulars just 
as experience does. Therefore the aforesaid difference pertains only to the way in which they 
come to know. But even though art and experience do not differ in the way in which they act, 
because both act on singular things, nevertheless they differ in the effectiveness of their 
action. For men of experience act more effectively than those who have the universal 
knowledge of an art but lack experience. 

21. The reason is that actions have to do with singular things, and all processes of generation 
belong to singular things. For universals are generated or moved only by reason of something 
else, inasmuch as this belongs to singular things. For man is generated when this man is 
generated. Hence a physician heals man only incidentally, but properly he heals Plato or 
Socrates, or some man that can be individually named, to whom the nature man belongs, or 
rather to whom it is accidental inasmuch as he is the one healed. For even though the nature 
man belongs essentially to Socrates, still it belongs only accidentally to the one healed or 
cured; for the proposition "Socrates is a man" is an essential one, because, if Socrates were 
defined, man would be given in his definition, as will be said below in Book IV." But the 
proposition "What is healed or cured is man" is an accidental one. 


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22. Hence, since art has to do with universals and experience with singulars, if anyone has the 
theoretical knowledge of an art but lacks experience, he will be perfect insofar as he knows 
the universal; but since he does not know the singular, because he lacks experience, he will 
very often make mistakes in healing. For healing belongs to the realm of the singular rather 
than to that of the universal, because it belongs to the former essentially and to the latter 
accidentally. 

23. Yet we think (8). 

Here he compares art with experience from the viewpoint of knowing; and in regard to this he 
does two things. First (23), he states how art is superior to experience; and second (24), he 
proves this ("Now this is because"). 

He claims that art and science are superior to experience in three respects. First, they are 
superior from the viewpoint of scientific knowledge, which we think is attained by art rather 
than by experience. Second, they are superior from the viewpoint of meeting objections, 
which occurs in disputes. For in a dispute the one who has an art is able to meet the objections 
raised against that art, but one who has experience [alone] cannot do this. Third, they are 
superior from this point of view, that those who have an art come nearer to the goal of 
wisdom than men of experience, "Implying that it is," i.e., happens to be, "more truly to know 
if wisdom pursues all things," i.e., insofar as it pursues universals. For one who has an art is 
judged wiser than one who has experience, by reason of the fact that he considers universals. 
Or in another version: "Implying that it is more according to wisdom to know as one pursuing 
all things," i.e., universals. Another reading has: "As more conformable to knowing, since 
wisdom pursues all things," as if to say: "As more dependent upon knowing" than upon 
doing, "since wisdom pursues all things," i.e., it seeks to reach each single thing; so that those 
are rather called wise who are more knowing, not those who are more men of action. Hence 
another reading expresses this meaning more clearly, saying: "Implying that all pursue 
wisdom more with respect to knowing." 

24. Now this is (9). 

Then he proves the superiority of art and science mentioned above, and he does this by means 
of three arguments. The first runs thus: those who know the cause and reason why a thing is 
so are more knowing and wiser than those who merely know that it is so but do not know 
why. Now men of experience know that something is so but do not know the reason, whereas 
men who have an art know not merely that something is so but also know its cause and 
reason. Hence those who have an art are wiser and more knowing than those who have 
experience. 

25. For this reason too (9). 

Here he proves the first aspect of superiority, and this runs as follows. Those who know the 
cause and reason why a thing is so are compared to those who merely know that it is so as the 
architectonic arts are to the arts of manual laborers. But the architectonic arts are nobler. In a 
similar way, then, those who know the causes and reasons of things are more knowing than 
those who merely know that things are so. 

26. The first part of this proof becomes clear from the fact that architects, or master artists, 
know the causes of the things that are done. In order to understand this we must note that 
architect means chief artist, from meaning chief, and meaning art. Now that 


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art is said to be a chief art which performs a more important operation. Indeed, the operations 
of artists are distinguished in this way; for some operations are directed to disposing the 
material of the artifact. Carpenters, for example, by cutting and planing the wood, dispose 
matter for the form of a ship. Another operation is directed to introducing this form into the 
matter, for example, when someone builds a ship out of wood which has been disposed and 
prepared. A third operation is directed to the use of the finished product, and this is the 
highest operation. But the first operation is the lowest because it is directed to the second and 
the second to the third. Hence the shipbuilder is a superior artist compared with the one who 
prepares the wood; and the navigator, who uses the completed ship, is a superior artist 
comparedwith the shipbuilder. 

27. Further, since matter exists for the sake of form, and ought to be such as to befit the form, 
the shipbuilder knows the rea son why the wood should be shaped in some particular way; but 
those who prepare the wood do not know this. And in a similar way, since the completed ship 
exists in order to be used, the one who uses the ship knows why it should have some 
particular form; for the form should be one that befits its use. Thus it is evident that the reason 
for the operations which dispose the matter is taken from the design of the product in the 
artist's mind, and the reason for the operations which produce the form of the artifact is taken 
from the use [to which the artifact is put] . 

28. It is evident, then, that the master artists know the causes of the things which are done. In 
fact we judge and speak about the others, i.e., the manual laborers, as we do about certain 
inanimate things. This is not because they do not perform artful operations, but because the 
things which they do they do without knowing the cause; for they know that something is to 
be done but not why it is, just as fire burns without knowing why. Hence there is a likeness 
between inanimate things and manual laborers from this point of view, that, just as inanimate 
things act without knowing the causes, inasmuch as they are directed to their proper end by a 
superior intellect, so also do manual laborers. But they differ in this respect, that inanimate 
things perform each of their operations as a result of their nature, whereas manual laborers 
perform theirs through habit. And while habit is practically the same as nature inasmuch as it 
is inclined to one definite effect, still habit differs from nature inasmuch as it is open to 
opposites by reason of human knowledge. For we do not habituate natural bodies, as is stated 
in Book II of the Ethics; nor, indeed, is it possible to cause habits in things that lack 
knowledge. Now the statements that have been made, as is evident from the statements 
themselves, must be interpreted as meaning that some men are wiser, not insofar as they are 
"practical," i.e., men of action, as befits men of experience, but insofar as they have a plan for 
things to be done and know their causes, which are the basis of such a plan; and this befits 
master artists. 

29. In general a sign of scientific knowledge (10). 

Here he gives the second argument, which is as follows: a sign of knowledge is the ability to 
teach, and this is so because each thing is perfect in its activity when it can produce another 
thing similar to itself, as is said in Book IV of Meteors. Therefore, just as the possession of 
heat is indicated by the fact that a thing can heat something else, in a similar way the 
possession of knowledge is indicated by the fact that one can teach, that is, cause knowledge 
in another. But men who have an art can teach, for since they know causes they can 
demonstrate from these; and demonstration is a syllogism which produces knowledge, as is 
said in Book I of the Posterior Analytics . But men who have experience [only] cannot teach; 
for since they do not know the causes, they cannot cause knowledge in someone else. And if 
they do teach others the things which they know by experience, these things are not learned 


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after the manner of scientific knowledge but after that of opinion or belief. Hence, it is clear 
that men who have an art are wiser and more knowing than those who have experience. 

30. Furthermore, we do not hold (11). 

Here he gives the third argument, which is as follows: knowing singular things is proper to 
the senses rather than to any other type of knowing [power] , since our entire knowledge of 
singular things originates with the senses. Yet we do not hold that "any one of these," i.e., any 
one of the senses, is wisdom, because even though each sense knows that a thing is so, it does 
not know why it is so; for touch judges that fire is hot but does not know why it is hot. 
Therefore men of experience, who have a knowledge of singular things but do not know their 
causes, cannot be called wise men. 

31. It is only fitting (12). 

Here he compares practical art with speculative art; and in regard to this he does three things. 
First (20), he shows that a speculative art is wisdom to a greater degree than a practical art. 
Second (ibid.), he answers an objection ("The difference"). 

He proves his first statement by this argument: in any of the sciences or arts we find that men 
with scientific knowledge are more admired and are held in higher esteem than all other men, 
because their knowledge is held to be nobler and more worthy of the name of wisdom. Now 
the discoverer of any art at all is admired because he perceives, judges and discerns a cause 
beyond the perceptions of other men, and not because of the usefulness of his discoveries. We 
admire him rather "as being wise, and as distinguishing [a thing] from others." As being wise, 
indeed, in the subtle way in which he investigates the causes of his discoveries, and as 
distinguishing [a thing] from others insofar as he investigates the ways in which one thing 
differs from another. Or, according to another interpretation, "as being distinct from the 
others" is to be read passively, as being distinguished in this respect from others. Hence 
another text has "one who is different." Some sciences, then, are more admirable and worthy 
of the name of wisdom because their observations are more outstanding, not because they are 
useful. 

32. Therefore, since many useful arts have been discovered (some to provide the necessities 
of life, as the mechanical arts, and others to introduce us to the sciences, as the logical 
disciplines), those artists must be said to be wiser whose sciences were discovered not for the 
sake of utility but merely for the sake of knowing, that is to say, the speculative sciences. 

33. That the speculative sciences were not discovered for the sake of utility is made clear by 
this fact, that after all sciences of this kind "had already been developed," i.e., acquired or 
discovered, which can serve as introductions to the other sciences, or provide the necessities 
of life, or give pleasure (as those arts whose object is to delight man), the speculative sciences 
were discovered, not for this kind of end, but for their own sake. The fact that they were not 
discovered for the sake of utility becomes evident from the place in which they were 
discovered. For they originated in those places where men first applied themselves to such 
things. Another version reads, "And first in those places where men had leisure," i.e., they 
had time for study because they were released from other occupations as a result of the 
abundance of things necessary [for life]. Hence the mathematical arts, which are speculative 
in the highest degree, were first discovered in Egypt by the priests, who were given time for 
study, and whose expenses were defrayed by the community, as we also read in Genesis 
(47:22) 


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34. But because the names "wisdom," "science" and "art" have been used indifferently, lest 
someone should think that these terms are synonymous, he excludes this opinion and refers to 
his work on morals, i.e., to Book VI of the Ethics, where he has explained the difference 
between art, wisdom, science, prudence, and understanding. And to give the distinction 
briefly — wisdom, science and understanding pertain to the speculative part of the soul, which 
he speaks of in that work as the scientific part of the soul. But they differ in that 
understanding is the habit of the first principles of demonstration, whereas science has to do 
with conclusions drawn from subordinate causes, and wisdom with first causes. This is the 
reason it is spoken of there as the chief science. But prudence and art belong to the practical 
part of the soul, which reasons about our contingent courses of action. And these also differ; 
for prudence directs us in actions which do not pass over into some external matter but are 
perfections of the one acting (which is the reason why prudence is defined in that work as the 
reasoned plan of things to be done), but art directs us in those productive actions, such as 
building and cutting, which pass over into external matter (which is the reason why art is 
defined as the reasoned plan of things to be made). 

Wisdom deals with causes. 

35. From what has been said he proves his major thesis, that is to say, that wisdom deals with 
the causes of things. He says that the reason "for undertaking this investigation," i.e., the 
above piece of reasoning, is that the science which is called wisdom seems to be about first 
causes and principles. This is evident from the foregoing; for the more a man attains to a 
knowledge of the cause, the wiser he is. This is also evident from the foregoing; because the 
man of experience is wiser than one who has sensation alone without experience; and the 
artist is wiser than any man of experience; and among artists the architect is wiser than the 
manual laborer. And similarly among the arts and sciences the speculative are more scientific 
than the practical. All these things are dear from the foregoing remarks. It follows, then, that 
that science which is wisdom in an absolute sense is concerned with the causes of things. The 
method of arguing would be similar if we were to say that that which is hotter is more afire, 
and therefore that that which is afire in an absolute sense is hot in an absolute sense. 


LESSON 2 

Wisdom Considers Universal First Causes and First Principles 
ARISTOTLE'S TEXT Chapter 2: 982a 4-982b 11 

14. But since we are in search of this science, it will therefore be necessary to consider with 
what kind of causes and principles wisdom or science deals. This will perhaps become 
evident if we take the opinions which we have about the wise man. First of all, then, we think 
that the wise man is one who knows all things in the highest degree, as becomes him, without 
having a knowledge of them individually. 

15. Next, we say that that man is wise who is capable of knowing things that are difficult and 
not easy for man to understand. For sensory perception is common to all, and is therefore easy 
and not a matter of wisdom. 


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16. Again, [we consider him wise who is] more certain. 

17. And in every branch of science we say that he is wiser who is more capable of teaching us 
about the causes of things. 

18. Again, among the sciences we think that that science which exists for itself and is 
desirable for the sake of knowledge is wisdom to a greater degree than one which is desirable 
for the sake of contingent effects. 

19. And we think that a superior science which is rather the more basic comes nearer to 
wisdom than a subordinate science. For a wise man must not be directed but must direct, and 
he must not obey another but must be obeyed by one who is less wise. Such then and so many 
are the opinions which we have about the wise and about wisdom. 

20. Now of these attributes, that of knowing all things necessarily belongs to him who has 
universal knowledge in the highest degree, because he knows in which are subordinate. 

21. But the things which are just about the most difficult for man to understand are also those 
which are most universal; for they are farthest removed from the senses. 

22. Again, the most certain of the sciences are those which are most concerned with primary 
things. For sciences based on fewer principles are more certain than those which have 
additional principles, as arithmetic is more certain than geometry. 

23. Moreover, that science which speculates about the causes of things is more instructive. 
For those who teach us are those who assign the causes of every single thing. 

24. Again, understanding and scientific knowledge for their own sake are found in the highest 
degree in the science which has as its object what is most knowable. For one who desires 
scientific knowledge for itself will desire in the highest degree the science which is most truly 
science, and such a science has for its object what is most knowable. Now first principles and 
causes are most knowable; for it is by reason of these and from these that other things are 
known, and not these from things which are subordinate to them. 

25. But that science is highest and superior to subordinate sciences which knows the reason 
why each single thing must be done. This is the good of every single thing, and viewed 
universally it is the greatest good in the whole of nature. 

26. In view of everything that has been said, then, the term which we are investigating 
evidently falls to the same science. For this science must speculate about first principles and 
causes, because the good, or that for the sake of which something is done, is also one of the 
causes. 

COMMENTARY 

Six opinions about who is wise 

36. Having shown that wisdom is a knowledge of causes, the Philosopher's aim here is to 
establish with what kinds of causes and what kinds of principles it is concerned. He shows 
that it is concerned with the most universal and primary causes, and he argues this from the 
definition of wisdom. 


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In regard to this he does three things. First, he formulates a definition of wisdom from the 
different opinions which men have about the wise man and about wisdom. Second (44), he 
shows that all of these are proper to that universal science which considers first and universal 
causes ("Now of these"). Third (50), he draws the conclusion at which he aims ("In view of 
everything"). In regard to the first he gives six common opinions which men have entertained 
about wisdom. 

He states the first where he says "But since we are in search"; and this opinion is this: in 
general we all consider those especially to be wise who know all things, as the case demands, 
without having a knowledge of every singular thing. For this is impossible, since singular 
things are infinite in number, and an infinite number of things cannot be comprehended by the 
intellect. 

37. Next, we say that (15). 

Here he gives the second opinion, which is this: we hold that man to be wise who is capable, 
by reason of his intellect, of knowing difficult things, and those which are not easy for 
ordinary men to understand. For sensory perception, i.e., the knowing of sensible things, is 
common to all men, and is therefore easy and so not a matter of wisdom. That is to say, it is 
neither a mark nor the office of a wise man. Thus it is clear that whatever pertains properly to 
wisdom is not easily known by all. 

38. Again, [we consider] (16). 

Here he gives the third opinion, namely, that we say that he is wise who, regarding what he 
knows, is more certain than other men generally are. 

39. And in every branch (17). Here he gives the fourth opinion, namely, that that man is said 
to be wiser in every science who can give the causes of anything that is brought into question, 
and can teach by means of this. 

40. Again, among the sciences (18). 

Here he gives the fifth opinion, which is this: among the many sciences that science which is 
more desirable and willed for its own sake, i.e., chosen for the sake of knowledge and for 
knowledge itself alone, is more of the nature of wisdom than one which is for the sake of any 
of the other contingent effects which can be caused by knowledge, such as the necessities of 
life, pleasure, and so forth. 

41. And we think (19). Here he gives the sixth opinion, namely, that this wisdom, of which 
mention has been made, must be or is said to be "rather the more basic," i.e., nobler, than "a 
subordinate science." This can be understood from the foregoing. For in the field of the 
mechanical arts, subordinate artists are those who execute by manual operations the 
commands of superior artists, whom he referred to above as master artists and wise men. 

42. That the notion of wisdom belongs to sciences which give orders rather than to those 
which take them, he proves by two arguments. The first is that subordinate sciences are 
directed to superior sciences. For subordinate arts are directed to the end of a superior art, as 
the art of horsemanship to the end of the military art. But in the opinion of all it is not fitting 
that a wise man should be directed by someone else, but that he should direct others The 
second is that inferior artists are induced to act by superior artists inasmuch as they rely upon 


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superior artists for the things which they must do or make. Thus the shipbuilder relies upon 
the instructions of the navigator for the kind of form which a ship ought to have. However, it 
does not befit a wise man that he should be induced to act by someone else, but that he should 
use his knowledge to induce others to act. 

43. These, then, are the kind of opinions which men have of wisdom and the wise; and from 
all of these a description of wisdom can be formulated, so that the wise man is described as 
one who knows all, even difficult matters, with certitude and through their cause; who seeks 
this knowledge for its own sake; and who directs others and induces them to act. And in this 
way the major premise of the syllogism becomes evident. For every wise man must be such, 
and conversely whoever is such is wise. 

These six attributes are found in the metaphysician. 

44. Now of these (20). Here he shows that all of the above attributes come together in the 
man who knows the first and universal causes of things; and he follows the same order as he 
did above. Thus he held first that knowledge of all things in the highest degree belongs to him 
who has universal knowledge. This was the first opinion, and it is made clear in this way: 
Whoever knows universals knows in some respect the things which are subordinate to 
universals, because he knows the universal in them. ' But all things are subordinate to those 
which are most universal. Therefore the one who knows the most universal things, knows in a 
sense all things. 

45. But the things (21). 

Here he proves that the second attribute belongs to the same person, by the following 
argument. Those things which are farthest removed from the senses are difficult for men to 
know; for sensory perception is common to all men since all human knowledge originates 
with this. But those things which are most universal are farthest removed from sensible 
things, because the senses have to do with singular things. Hence universals are the most 
difficult for men to know. Thus it is clear that that science is the most difficult which is most 
concerned with universals. 

46. But the statement which appears in Book I of the Physics seems to contradict this. For it is 
said there that more universal things are known first by us; and those things which are known 
first are those which are easier. Yet it must be said that those things which are more universal 
according to simple apprehension are known first; for being is the first thing that comes into 
the intellect, as Avicenna says, and animal comes into the intellect before man does. For just 
as in the order of nature, which proceeds from potentiality to actuality, animal is prior to man, 
so too in the genesis of knowledge the intellect conceives animal before it conceives man. 

But with respect to the investigations of natural properties and causes, less universal things 
are known first, because we discover universal causes by means of the particular causes 
which belong to one genus or species. Now those things which are universal in causing are 
known subsequently by us (notwithstanding the fact that they are things which are primarily 
knowable according to their nature), although things which are universal by predication are 
known to us in some way before the less universal (notwithstanding the fact that they are not 
known prior to singular things). For in us sensory knowledge, which is cognitive of singular 
things, precedes intellective knowledge, which is about universals. And some importance 
must also be attached to the fact that he does not say that the most universal things are the 
most difficult absolutely, but "just about." For those things which are entirely separate from 


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matter in being, as immaterial substances, are more difficult for us to know than universals. 
Therefore, even though this science which is called wisdom is the first in dignity, it is still the 
last to be learned. 

47. Again, the most certain (22). 

Here he shows that the third attribute belongs to the same science, by this argument: the more 
any sciences are prior by nature, the more certain they are. This is clear from the fact that 
those sciences which are said to originate as a result of adding something to the other sciences 
are less certain than those which take fewer things into consideration; for example, arithmetic 
is more certain than geometry because the objects considered in geometry are a result of 
adding to those considered in arithmetic. This becomes evident if we consider what these two 
sciences take as their first principle, namely, the point and the unit. For the point adds to the 
unit the notion of position, because undivided being constitutes the intelligible structure of the 
unit; and insofar as this has the function of a measure it becomes the principle of number. 
And the point adds to this the notion of position. However, particular sciences are subsequent 
in nature to universal sciences, because their subjects add something to the subjects of 
universal sciences. For example, it is evident that mobile being, with which the philosophy of 
nature deals, adds to being pure and simple, with which metaphysics is concerned, and to 
quantified being, with which mathematics is concerned. Hence that science which treats of 
being and the most universal things is the most certain. Moreover, the statement here that this 
science deals with fewer principles is not opposed to the one made above, that it knows all 
things; for the universal takes in fewer inferiors actually, but many potentially. And the more 
certain a science is, the fewer actual things it has to consider in investigating its 
subject-matter. Hence the practical sciences are the least certain, because they must consider 
the many circumstances attending individual effects. 

48. Moreover, that science (23). 

Here he proves that the fourth attribute belongs to the same science, by this argument: that 
science is more instructive, or better able to teach, which is concerned to a greater degree with 
causes. For only those teach who assign the causes of every single thing, because scientific 
knowledge comes about through some cause, and to teach is to cause knowledge in another. 
But that science which considers universals considers the first of all the causes. Hence it is 
evidently the best fitted to teach. 

49. Again, understanding (24). 

Here he proves that the fifth attribute belongs to the same science, by this argument: it is the 
office of those sciences which deal with things that are most knowable, most properly to 
know and understand for their own sake, i.e., for the sake of those sciences themselves and 
not for something else. But it is the sciences that deal with first causes which consider the 
most knowable things. Therefore those sciences are desired most for their own sake. He 
proves the first premise thus: One who most desires knowledge for the sake of knowledge 
most desires scientific knowledge. But the highest kind of knowledge is concerned with 
things that are most knowable. Therefore those sciences are desired most for their own sake 
which have to do with things that are most knowable. He proves the second premise thus: 
Those things from which and by reason of which other things are known are more knowable 
than the things which are known by means of them. But these other things are known through 
causes and principles, and not vice versa, etc. 


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50. But that science (25). 

Here he proves that the sixth attribute belongs to the same science, by the following 
argument: that science which considers the final cause, or that for the sake of which particular 
things are done, is related to the other sciences as a chief or master science is to a subordinate 
or ancillary one, as is evident from the foregoing remarks. For the navigator, to whom the use, 
or end, of the ship belongs, is a kind of master artist in relation to the shipbuilder who serves 
him. But the aforesaid science is concerned most with the final cause of all things. This is 
dear from the fact that that for the sake of which all particular things are done is the good of 
each, i.e., a particular good. But the end in any class of things is a good; and that which is the 
end of all things, i.e., of the universe itself, is the greatest good in the whole of nature. Now 
this belongs to the consideration of the science in question, and therefore it is the chief or 
architectonic science with reference to all the others. 

51. In view of everything (26). Here he draws from the foregoing arguments his intended 
conclusion, saying that it is clear from everything that has been said that the name wisdom 
which we are investigating belongs to the same science which considers or speculates about 
first principles and causes. This is evident from the six primary conditions which clearly 
pertain to the science that considers universal causes. But because the sixth condition touched 
on the consideration of the end, which was not clearly held to be a cause among the ancient 
philosophers, as will be said below (1 177), he therefore shows in a special way that this 
condition belongs to the same science, namely, the one which considers first causes. For the 
end, which is a good and that for the sake of which other things are done, is one of the many 
causes. Hence the science which considers first and universal causes must also be the one 
which considers the universal end of all things, which is the greatest good in the whole of 
nature. 


LESSON 3 

The Nature and Goal of Metaphysics 
ARISTOTLE'S TEXT Chapter 2: 982b ll-983a 23 

27. That this is not a practical science is evident from those who first philosophized. For it is 
because of wonder that men both now and formerly began to philosophize, about less 
important matters, and then progressing little by little, they raised questions about more 
important ones, such as the phases of the moon and the courses of the sun and the stars and 
the generation of the universe. But one who raises questions and wonders seems to be 
ignorant. Hence the philosopher is also to some extent a lover of myth, for myths are 
composed of wonders. If they philosophized, then, in order to escape from ignorance, they 
evidently pursued their studies for the sake of knowledge and not for any utility. 

28. And what has happened bears witness to this; for when nearly all the things necessary for 
life, leisure and learning were acquired, this kind of prudence began to be sought. It is 
evident, then, that we do not seek this knowledge for the sake of any other necessity. 


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29. But just as we say that a man is free who exists for himself and not for another, in a 
similar fashion this is the only free, science, because it alone exists for itself. 

30. For this reason, too, it might rightly be thought that this science is not a human 
possession, since in many respects human nature is servile. 

31. Hence, according, to Simonides, "Only God has this honor," I and it is unfitting that a 
man should not seek a knowledge which befits him. Some poets accordingly say that the deity 
is naturally envious; and it is most likely that it should happen in this case, and that all those 
who are imperfect are unfortunate. But it is not fitting that the deity should be envious, for as 
the proverb says: "The poets tell many lies." 

32. Nor must we think that any other science is more honorable than this. For what is most 
divine is most honorable. But then it alone will be such, and in two ways. For of all 
knowledge that which God most properly has is divine; and if there is any such knowledge, it 
is concerned with divine matters. But this science alone has both of these characteristics; for 
God seems to be a cause and in some sense a principle according to all men; and such 
[knowledge as this] God either alone has, or has in the highest degree. Therefore, all the other 
sciences are more necessary, but none is more excellent. 

33. But it is necessary in a sense to bring to a halt the progression of this science at the 
contrary of our original questions. Indeed, as we have said, all men begin by wondering 
whether things are as strange as chance occurrences appear to those who do not yet know the 
cause; or by wondering about the changes in the course of the sun, or about the 
incommensurability of the diagonal [of a square]. For it would seem an object of wonder to 
all it something having the nature of number were immeasurable. But it is necessary to 
advance to the contrary view and, as the proverb says, the worthier one, as also happens in a 
sense in these matters when men have learned them. For nothing would surprise a 
geometrician more than if the diagonal [of a square] should become commensurable [with a 
side] . It has been stated, then, what the nature is of the science which we are seeking, and 
what its goal is for which our search and whole method must be undertaken. 

COMMENTARY 

Why this science is called speculative 

53. First, he gives this argument. No science in which knowledge itself is sought for its own 
sake is a practical science, but a speculative one. Bot that science which is wisdom, or 
philosophy as it is called, exists for the sake of knowledge itself. Hence it is speculative and 
not practical. He proves the minor premise in this way. Whoever seeks as an end to escape 
from ignorance tends toward knowledge for itself. But those who philosophize seek as an end 
to escape from ignorance. Therefore they tend towards knowledge for itself. 

54. That they seek to escape from ignorance is made clear from the fact that those who first 
philosophized and who now philosophize did so from wonder about some cause, although 
they did this at first differently than now. For at first they wondered about less important 
problems, which were more obvious, in order that they might know their cause; but later on, 
progressing little by little from the knowledge of more evident matters to the investigation of 
obscure ones, they began to raise questions about more important and hidden matters, such as 
the changes undergone by the moon, namely, its eclipse, and its change of shape, which 
seems to vary inasmuch as it stands in different relations to the sun. And similarly they raised 


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questions about the phenomena of the sun, such as its eclipse, its movement and size; and 
about the phenomena of the stars, such as their size, arrangement, and so forth; and about the 
origin of the whole universe, which some said was produced by chance, others by an 
intelligence, and others by love. 

55. Further, he points out that perplexity and wonder arise from ignorance. For when we see 
certain obvious effects whose cause we do not know, we wonder about their cause. And since 
wonder was the motive which led men to philosophy, it is evident that the philosopher is, in a 
sense, a philo-myth, i.e., a lover of myth, as is characteristic of the poets. Hence the first men 
to deal with the principles of things in a mythical way, such as Perseus and certain others who 
were the seven sages, were called the theologizing poets. Now the reason why the philosopher 
is compared to the poet is that both are concerned with wonders. For the myths with which 
the poets deal are composed of wonders, and the philosophers themselves were moved to 
philosophize as a result of wonder. And since wonder stems from ignorance, they were 
obviously moved to philosophize in order to escape from ignorance. It is accordingly evident 
from this that "they pursued" knowledge, or diligently sought it, only for itself and not for any 
utility or usefulness. 

56. Now we must note that, while this science was first designated by the name wisdom, this 
was later changed to the name philosophy, since they mean the same thing. For while the 
ancients who pursued the study of wisdom were called sophists, i.e., wise men, Pythagoras, 
when asked what he professed himself to be, refused to call himself a wise man as his 
predecessors had done, because he thought this was presumptuous, but called himself a 
philosopher, i.e., a lover of wisdom. And from that time the name "wise man" was changed to 
"philosopher," and "wisdom" to "philosophy." This name also contributes something to the 
point under discussion, for that man seems to be a lover of wisdom who seeks wisdom, not 
for some other reason, but for itself alone. For he who seeks one thing on account of 
something else, has greater love for that on whose account he seeks than for that which he 
seeks. 

57. And what has happened (28). 

Here he proves the same point by means of an example. The statement (he says) that wisdom 
or philosophy is not sought for any utility but for knowledge itself is proved by "what has 
happened," i.e., by what has occurred in the case of those who have pursued philosophy. For 
when nearly all those [arts] were discovered which are necessary for life, "leisure" (i.e., for 
the sort of pleasure which consists in a life of ease), and learning, such as the logical sciences, 
which are not sought for themselves but as introductions to the other arts, then man began for 
the first time to seek this kind of prudence, namely, wisdom. And from this it is clear that 
wisdom is not sought because of any necessity other than itself but for itself a one; for no one 
seeks something which he already possesses. Hence, because wisdom was sought after all 
other knowledge had been discovered, it is evident that it was not sought for some reason 
other than itself but for itself. 

Why this science is liberal 

58. But just as (29). 

Here he proves the second attribute, namely, that wisdom is free; and he uses the following 
argument: that man is properly said to be free who does not exist for someone else but for 
himself. For slaves exist for their masters, work for them, and acquire for them whatever they 


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acquire. But free men exist for themselves inasmuch as they acquire things for themselves 
and work for themselves. But only this science exists for itself; and therefore among all the 
sciences only this science is free. 

59. Now we must note that this can be understood in two ways. In one way, the expression 
"only this" may indicate every speculative science as a class. And then it is true that only this 
class of science is sought for itself. Hence, only those arts which are directed to knowing are 
called free [or liberal] arts, whereas those which are directed to some useful end attained by 
action are called mechanical or servile arts. 

Understood in another way, the expression may specifically indicate this philosophy or 
wisdom which deals with the highest causes; for the final cause is also one of the highest 
causes, as was stated above (51). Therefore this science must consider the highest and 
universal end of all things. And in this way all the other sciences are subordinated to it as an 
end. Hence only this science exists in the highest degree for itself. 

Why this science is super-human 

60. For this reason (30). 

Here he proves the third attribute, namely, that this science is not a human [possession]. In 
regard to this he does two things. First, he proves his thesis. Second (61), he criticizes an 
erroneous view held by certain men ("Hence, according to Simonides"). 

He proves his thesis by the following argument. A science which is free in the highest degree 
cannot be a possession of that nature which is servile and subordinate in many respects. But 
human nature is servile "in many respects," i.e., in many ways. Therefore this science is not a 
human possession. Now human nature is said to be servile insofar as it stands in need of many 
things. And on this account it happens that man sometimes neglects what should be sought for 
its own sake because of the things necessary for life. Thus it is said in Book III of the Topics 
that it is better to philosophize than to become wealthy, although sometimes becoming 
wealthy is more desirable, that is, to one lacking life's necessities. From this it is clear that 
that wisdom is sought for itself alone which does not belong to man as his proper possession. 
For man has as his possession what he can have at his command and use freely. But that 
science which is sought for itself alone, man cannot use freely, since he is often kept from it 
because of the necessities of life. Nor again is it subject to man's command, because man 
cannot acquire it perfectly. Yet that very small part of it which he does have outweighs all the 
things known through the other sciences. 

61. Hence, according to Simonides (31). 

Here he rejects the error of a certain poet, Simonides, who said that it is proper to God alone 
to have the honor of desiring that knowledge which ought to be sought for its own sake and 
not for the sake of something else. But it is not fitting that man should not seek that 
knowledge which is in keeping with his own condition, namely, that which is directed to the 
necessities of life required by man. 

62. Now Simonides' error came from that of certain poets who said that the Deity is envious, 
and that since He is envious He does not desire that the things which pertain to His honor 
should be shared by all. And if God is envious of men in other things, He is rightly more so in 
this case, i.e., in the case of the science which is sought for its own sake, which is the most 


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honorable of all the sciences. And according to the opinion of these men it follows that all 
who are imperfect are unfortunate' for they said that men are fortunate as a result of the 
providence of the gods, who communicate their goods to men. Hence as a result of the envy 
of the gods, who are unwilling to communicate their goods, it follows that men, who remain 
outside the perfection of this science, are unfortunate. 

63. But the basis of this opinion is most false, because it is not fitting that any divine being 
should be envious. This is evident from the fact that envy is sadness at someone else's 
prosperity. But this can occur only because the one who is envious thinks that someone else's 
good diminishes his own. Now it is impossible that God' should be sad, because He is not 
subject to evil of any kind. Nor can His goodness be diminished by someone else's goodness, 
since every good flows from His goodness as from an unfailing spring. Hence Plato also said 
that there is no envy of any kind in God.' But the poets have lied not only in this matter but in 
many others, as is stated in the common proverb. 

Why this science is most honorable 

64. Nor must we think (32). 

Here he proves the fourth attribute, namely, that this is the most honorable science, by the 
following argument. That science which is most divine is most honorable, just as God 
Himself is also the most honorable of all things. But this science is the most divine, and is 
therefore the most honorable. The minor premise is proved in this way: a science is said to be 
divine in two ways, and only this science is said to be divine in both ways. First, the science 
which God has is said to be divine; and second, the science which is about divine matters is 
said to be divine. But it is evident that only this science meets both of these requirements, 
because, since this science is about first causes and principles, it must be about God; for God 
is understood in this way by all inasmuch as He is one of the causes and a principle of things. 
Again, such a science which is about God and first causes, either God alone has or, if not He 
alone, at least He has it in the highest degree. Indeed, He alone has it in a perfectly 
comprehensive way. And He has it in the highest degree inasmuch as it is also had by men in 
their own way, although it is not had by them as a human possession, but as something 
borrowed from Him. 

65. From these considerations he draws the further conclusion that all other sciences are more 
necessary than this science for use in practical life, for these sciences are sought least of all 
for themselves. But none of the other sciences can be more excellent than this one. 

The relation between wonder and wisdom 

66. But it is necessary (33). 

He now gives the goal toward which this science moves. He says that its progression comes 
to rest, or is terminated, in the contrary of what was previously found in those who first 
sought this science, as also happens in the case of natural generations and motions. For each 
motion is terminated in the contrary of that from which the motion begins. Hence, since 
investigation is a kind of movement towards knowledge, it must be terminated in the contrary 
of that from which it begins. But, as was stated above (53), the investigation of this science 
began with man's wonder about all things, because the first philosophers wondered about less 
important matters and subsequent philosophers about more hidden ones. And the object of 
their wonder was whether the case was like that of strange chance occurrences, i.e., things 


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which seem to happen mysteriously by chance. For things which happen as if by themselves 
are called chance occurrences. For men wonder most of all when things happen by chance in 
this way, supposing that they were foreseen or determined by some cause. For chance 
occurrences are not determined by a cause, and wonder results from ignorance of a cause. 
Therefore when men were not yet able to recognize the causes of things, they wondered about 
all things as if they were chance occurrences; just as they wondered about changes in the 
course of the sun, which are two in number, namely, the solstices, that of winter and that of 
summer. For at the summer solstice the sun begins to decline toward the south, after 
previously declining toward the north. But at the winter solstice the opposite occurs. And they 
wondered also that the diagonal of a square is not commensurable with a side. For since to be 
immeasurable seems to belong to the indivisible alone (just as unity alone is what is not 
measured by number but itself measures all numbers), it seems to be a matter of wonder that 
something which is not indivisible is immeasurable, and consequently that what is not a 
smallest part is immeasurable. Now it is evident that the diagonal of a square and its side are 
neither indivisible nor smallest parts. Hence it seems a matter of wonder if they are not 
commensurable. 

67. Therefore, since philosophical investigation began with wonder, it must end in or arrive at 
the contrary of this, and this is to advance to the worthier view, as the common proverb 
agrees, which states that one must always advance to the better. For what that opposite and 
worthier view is, is evident in the case of the above wonders, because when men have already 
learned the causes of these things they do not wonder. Thus the geometrician does not wonder 
if the diagonal is incommensurable with a side. For he knows the reason for this, namely, that 
the proportion of the square of the diagonal to the square of a side is not as the proportion of 
the square of a number to the square of a number, but as the proportion of two to one. Hence 
it follows that the proportion of a side to the diagonal is not as the proportion of number to 
number. And from this it is evident that they cannot be made commensurable. For only those 
lines are commensurable which are proportioned to each other as number to number. Hence 
the goal of this science to which we should advance will be that in knowing the causes of 
things we do not wonder about their effects. 

68. From what has been said, then, it is evident what the nature of this science is, namely, that 
it is speculative and free, and that it is not a human possession but a divine one; and also what 
its aim is, for which the whole inquiry, method, and art must be conducted. For its goal is the 
first and universal causes of things, about which it also makes investigations and establishes 
the truth. And by reason of the knowledge of these it reaches this goal, namely, that there 
should be no wonder because the causes of things are known. 


LESSON 4 

Opinions about the Material Cause 
ARISTOTLE'S TEXT Chapter 3: 983a 24-984a 16 

34. It is evident, then, that one must acquire scientific knowledge of those causes which stand 
at the beginning, for we say that we have scientific knowledge of each thing when we think 
we comprehend its first cause. Now causes are spoken of in four ways. Of these we say that 


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one is the substance or quiddity of a thing, for the first "why" of a thing is reduced to its 
ultimate intelligible structure, and the first why of a thing is a cause or principle; another is 
the matter or subject; a third is the source of motion; and a fourth is the cause which is 
opposite to this, namely, that for the sake of which, or the good; for this is the goal of every 
generation and motion. There has been sufficient consideration of these in our works on 
nature. 

35. However, let us examine those who have undertaken an investigation of existing things 
and have philosophized about the truth before us. For evidently they too speak of certain 
principles and causes. Therefore, to us who come later [their views] will serve as an 
introduction to the study which we are now making; for we shall either discover some other 
class of cause, or be more convinced of those which have just been expounded. 

36. Most of those who first philosophized thought that only the things which belong to the 
class of matter are the principles of all things. For that of which all things are composed, from 
which they first come to be, and into which they are finally dissolved, while their substance 
remains although it is changed in its attributes — this they call the element and principle of 
existing things. 

37. And for this reason they thought that nothing is either generated or corrupted, as if such a 
reality always remained in existence. And just as we do not say that Socrates comes to be in 
an unqualified sense when he becomes good or musical, or is corrupted when he loses these 
states, because the subject Socrates himself remains, in the same way they say that nothing 
else is generated or corrupted. For there must be some matter, either one or more than one, 
from which other things come to be, and which itself remains in existence. However, they do 
not all speak in the same way about the number and nature of such a principle. 

38. Thales, the originator of this kind of philosophy, says that this principle is water; and this 
is why he also claimed that the earth rests upon water. 

39. For presumably he took this position because he saw that the nutriment of all things is 
moist, that heat itself is generated from this, and that animal life comes from this. But that 
from which each thing comes to be is a principle of all things. He bases his opinion on this, 
then, and on the fact that the seeds of all things have a moist nature, whereas water is by 
nature the principle of moist things. 

40. Moreover, there are some who think that the ancients who lived long before the present 
generation and were the first to speculate about the gods held this view about the nature of 
things. For they made Oceanus and Tethys the parents of generation, and held the oath of the 
gods to be by a body of water, to which the poets gave the name Styx. For what is oldest is 
most honorable, and what is most honorable is that by which one swears. Whether this view 
of nature is in fact the ancient and primary one is perhaps uncertain. Thales is said to have 
expressed himself in this way about the first cause, but no one could say that Hippo is to be 
included in this group, because of the weakness of his understanding. 

41. Anaximenes and Diogenes hold that air is prior to water and is the most fundamental of 
the simple bodies. 

42. Hippasus of Metopontium and Heraclitus of Ephesus hold that fire [is the primary 
principle] . 


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43. Empedocles holds that there are four [simple bodies], since he adds a fourth — earth — to 
those already mentioned. For he says that these always remain and only become many or few 
in number by being combined into a unity and separated out of a unity. 

44. Anaxagoras of Clazomenae, who was prior to Empedocles in years but later in his 
speculations, says that the principles of things are infinite in number. For he says that nearly 
all bodies which are made up of parts like themselves, such as fire or water, are generated or 
corrupted in this way, merely by combining and separating; but that otherwise they are 
neither generated nor corrupted but always remain in existence. From these views, then, one 
might think that the only cause is the one which is said to belong to the class of matter. 

COMMENTARY 

69. Having set f orth a preface in which he indicates the aim of this science, its dignity and 
goal, Aristotle begins to deal with this science; and this is divided into two parts. In the first 
(70), he explains what the first philosophers had to say about the causes of things. In the 
second (274), he begins to pursue the truth of this science. He does this in Book II 
("Theoretical, i.e., speculative, knowledge"). 

The first part is divided into two members. First, he gives the opinions of the philosophers 
about the causes of things. Second (181), he criticizes them insofar as their statements are 
unsatisfactory ("Therefore all those"). 

In regard to the firsthe does two things. First, he takes up again the enumeration of causes 
which was treated in greater detail in Book II of the Physics. Second (72), he presents the 
opinions of the philosophers ("However, let us examine"). 

The four causes, & three characteristics of final cause 

70. Accordingly, he says, first, that since it is evident that wisdom speculates about causes, 
we ought to begin by acquiring knowledge from the causes of things. This also seems to be in 
keeping with the intelligible structure of science, because we say that we know each thing 
scientifically when we think we are not ignorant of its cause. Now causes are spoken of in 
four ways. (1) One of these is the formal cause, which is the very substance of a thing by 
which we know what each thing is. For it is well known, as is stated in Book II of the Physics, 
that we do not say that anything has a nature before it has received a form. Now it is clear that 
a form is a cause, because the question "Why is something so?" we reduce to its formal cause 
as its ultimate explanation, beginning with proximate forms and proceeding to the ultimate 
form. But evidently the "why?" asks about a cause and principle. Hence it is evident that a 
form is a cause. (2) A second cause is the material cause. (3) A third is the efficient cause, 
which is the source of motion. (4) A fourth is the final cause, which is opposite to the efficient 
cause as a goal is to a starting-point; for motion begins with the efficient cause and terminates 
with the final cause. This [latter] cause is also that for the sake of which a thing comes to be, 
and the good of each nature. 

71. He makes the final cause known by three considerations: (1) It is the goal of motion, and 
thus is opposite to the source of motion, which is the efficient cause. (2) It is first in intention, 
and for this reason is said to be that for the sake of which [something is done]. (3) It is 
desirable of itself, and for this reason is called a good; for the good is what all desire. 


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Hence, in explaining how the final cause is opposite to the efficient cause, he says that it is 
the goal [or end] of every process of generation and motion, whose starting-point is the 
efficient cause. By these two types of change he seems to imply that there is a twofold goal: 
(1) For the goal of a process of generation is the form itself, which is a part of a thing. (2) But 
the goal of motion is something sought for outside the thing moved. He says that he has 
treated these causes at sufficient length in the Physics, lest he should be asked to make a more 
extensive treatment of them. 

72. However, let us examine (35). 

Here he states what the philosophers had to say about the causes; and in regard to this he does 
two things. First, he gives the reasons why this must be done; and, second (36:C 73), he 
begins to carry out his plan ("Most of those"). 

Accordingly, he says that even though there is a treatise on the causes in the Physics it is still 
necessary to consider the opinions of the philosophers who first undertook an investigation of 
the natures of existing things, and have philosophized about the truth before him; because 
they too set down causes and principles. Therefore, for us who have come later, a 
consideration of their opinions will be "a first [step]," or preamble, "to the investigation," i.e., 
to the art which we are now seeking. Hence the text of Boethius also says: "Therefore as we 
enter upon the task of this science, their opinions will constitute a prearn ble to the road that is 
now to be travelled." Another text has: "Therefore to us who are beginning this inquiry it will 
be a certain vital work in the investigation that now confronts us, " and it must be read in this 
way: "Therefore, as we enter upon our present course," i.e., upon the present study and art, it 
will be necessary to consider the opinion of these men "as a work of life," that is to say, as 
necessary, like works which are done for the preservation of life, so that this reading is 
interpreted as a metaphorical way of speaking, meaning by "work of life" anything necessary. 
Now this is useful, because from the opinions of these men we will either discover another 
class of causes over and above those already enumerated, or be more convinced of the things 
that have just been stated about the causes, namely, that there are four classes of them. 

73. Most of those (36). 

Here he begins to deal with the opinions of the ancient philosophers; and in regard to this he 
does two things. First (36), he states their opinions; and, second (86:C 181) he finds fault with 
them ("Therefore all those"). 

In regard to the first he does two things. First, he states the opinions which each one of the 
philosophers held about the causes. Second (79:C 170, he summarizes the discussion ("We 
have examined"). 

The first part is divided into two members. In the first (36:C 74), he gives the opinions of 
those who omitted the formal cause. In the second (69:C 151), he gives the opinion of Plato, 
who was the first to posit a formal cause ("After the philosophies"). 

In regard to the first he does two things. First, he gives the opinion of those who claimed that 
certain evident things are principles. Second (55:C , 12), he gives the opinions of those who 
devised extrinsic principles ("Leucippus"). 

In regard to the first he does two things. First, he touches on the opinions which the ancient 
philosophers held about the material cause; and, second (45:C 93), on their opinions about the 


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efficient cause ("But as men"). 

In regard to the first he does two things. First, he states in a general way the views of those 
who posited a material cause. Second (38:C 77), he examines their views in detail ("Thales, 
the originator"). 

In regard to the first he does two things. First, he states their opinions about the material 
cause. Second (37:C 75), he states their opinions about the generation of things, which follow 
from the first ("And for this reason"). 

OPINIONS OF THOSE WHO GAVE ONLY MATERIAL CAUSE 
Four characteristics of matter 

74. Accordingly he says, first (36), that most of those who first philosophized about the 
natural world held that the principles of all things are merely those which are referred to the 
class of material cause. In regard to this it must be said that they took the four conditions of 
matter which seem to belong to the notion of a principle. For, (1) that of which a thing is 
composed seems to be a principle of that thing. But matter is such a thing; for we say that a 
thing that has matter is of its matter, as a knife is of iron. (2) That from which a thing comes 
to be, being also a principle of the process of generation of that thing, seems to be one of its 
causes, because a thing comes into being by way of generation. But a thing first comes to be 
from matter, because the matter of things precedes their production. And a thing does not 
come from matter in an accidental way; for a thing is generated in an accidental way from its 
contrary or privation, as when we say that white comes from black. (3) Third, that into which 
all things are ultimately dissolved by corruption seems to be a principle of things. For just as 
principles are first in the process of generation, in a similar way they are last in the process of 
dissolution; and obviously this too pertains to matter. (4) Fourth, since a principle must 
remain in existence, then that which remains throughout the process of generation and 
corruption seems to be a principle. Now the matter which they said is the substance of a thing 
remains throughout every transmutation, although its attributes, such as its form and 
everything that accrues to it over and above its material substance, are changed. From all 
these considerations they concluded that matter is the element and principle of all beings. 

Without material cause, no generation or corruption 

75. And for this reason (37). 

Then he gives, as a secondary point, what they held as following from the above, namely, that 
in the world nothing is generated or corrupted in an absolute sense. For when some change 
occurs with regard to a thing's attributes, and its substance remains unchanged, we do not say 
that it is generated or corrupted in an absolute sense, but only in a qualified one; for example, 
when Socrates becomes good or musical, we do not say that he simply comes to be, but 
comes to be this. And similarly when he loses a state of this kind, we do not say that he is 
corrupted in an absolute sense, but only in a qualified one. But matter, which is the substance 
of things according to them, always remains; and every change affects some of a thing's 
accidents, such as its attributes. From this they concluded that nothing is generated or 
corrupted in an absolute sense, but only in a qualified one. 

76. Yet even though they all agreed on this point, in positing a material cause, nevertheless 
they differed in their position in two respects: first, with respect to the number of material 


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causes, because some held that there is one, and others many; and second, with respect to its 
nature, because some held that it is fire, others water, and so on. Similarly, among those who 
posited many material causes, some assigned certain ones as the material principles of things, 
and some the others. 

77. Thales, the originator (38). 

Here he begins to give the opinions of each of the philosophers about the material cause. 
First, he gives the opinions of those who posited one material cause; and second (88), the 
opinions of those who posited many ("Empedocles"). 

In regard to the first he does three things. First, he gives the opinions of those who claimed 
that water is the principle of all things; second (86), he gives the opinion of those who made 
air the principle of things ("Anaximenes"); and third (87), the opinion of those who claimed 
that fire is the principle of things ("Hippasus"). 

In regard to the first he does two things. First, he gives the opinion of Thales, who said that 
water is the principle of things; and second (79), the reason for this opinion ("For 
presumably"). 

He says then that Thales, the originator of this kind of philosophy, i.e., speculative 
philosophy, said that water is the first principle of all things. Thales is said to have been the 
originator of speculative philosophy because he was the only one of the seven wise men, who 
came after the theological poets, to make an investigation into the causes of things, the other 
sages being concerned with moral matters. The names of the seven wise men are as follows. 
The first was Thales of Miletus, who lived during the time of Romulus and when Achaz, King 
of Israel, was reigning over the Hebrews. The second was Pittacus of Mitylene, who lived 
when Sedecias was reigning over the Hebrews and when Tarquinius Priscus was reigning 
over the Romans. The other five sages were Solon of Athens, Chilo of Lacedaemon, 
Periander of Corinth, Cleobulus of Lydia, and Bias of Prienne, all of whom lived during the 
period of the Babylonian captivity. Hence, since Thales alone among these men investigated 
the natures of things and distinguished himself by committing his arguments to writing, he is 
described here as the originator of this science. 

78. Nor should it be thought unfitting if he touches here on the opinions of those who have 
treated only the philosophy of nature; because according to the ancients, who knew no other 
substance except the corporeal and mobile, it was necessary that first philosophy be the 
philosophy of nature, as is stated in Book IV. And from this position Thales next adopted this 
one, that the earth rests upon water, as anything having a principle is based on its principle. 

79. For presumably he took (39). 

Here he gives the reasons by which Thales could be led to the above position. First, he shows 
how he was led to this position by his own reasoning; and second (82), by the authority of his 
predecessors ("Moreover, there are some"). 

Now he was led by two lines of reasoning; one is taken from the cause itself of a thing, and 
the other from a consideration of the generation of things ("And on the fact"). Therefore these 
premises are related. For the second follows from the first, because that which is a principle 
of being of other things is also the first principle from which things are generated. The third 
follows from the second, because by corruption each thing is dissolved into that from which it 


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was generated. The fourth follows from the second and the third; for that which precedes the 
generation of things and remains after they have been corrupted must always remain in being. 

80. In the first line of reasoning he uses three indications to show that water is the principle of 
being of things. The first of these is that the nutriment of living things must be moist. But 
living things derive nourishment and being from the same principle; and thus moisture 
appears to be the principle of being of things. The second indication is that the being of any 
physical thing, and especially of a living one, is conserved by its proper and natural heat. But 
heat seems to be generated from moisture, since moisture itself is in a sense the matter of 
heat. Hence from this it appears that moisture is a principle of being of things. The third 
indication is that animal life depends on moisture. Hence an animal dies as a result of its 
natural moisture being dried up and is kept in existence as a result of its moisture being 
preserved. But in living things to live is to be. Hence it is also evident from this that moisture 
is a principle of being of things. These three indications also have a natural connection with 
one another. For an animal is nourished by moisture, because its natural heat is sustained by 
moisture. And from these two it follows that animal life is always due to moisture. But that 
from which a thing comes to be, i.e., from which a thing gets its being, is a principle of 
everything that derives being from it. And for this reason he adopted this opinion that 
moisture is the principle of all things. 

81. In a similar way he also draws an indication of this from the generation of things, because 
the processes of generation of living things, which are the noblest of [natural] beings, come 
from seed. But the seed or spermata of all living things have a moist nature. Hence from this 

it also appears that moisture is a principle of generation of things. Again, if we add to all of 
the above points the fact that water is the principle of moisture, it follows that water is the 
first principle of things. 

82. Moreover, there are (40). 

Here he shows how Thales was led to the above position by the authority of the ancients. He 
says that prior to Thales and many years before the men of Aristotle's time there were some 
men, the first to speculate about the gods, who seem to have held this opinion about nature, 
namely, that water is the principle of all things. 

83. With a view to making this clear, we must bear in mind that among the Greeks the first 
who were famous for their learning were certain theological poets, so called because of the 
songs which they wrote about the gods. These poets, who were three in number, Orpheus, 
Museus and Linus, of whom Orpheus was the more famous, lived during the time when the 
judges ruled over the Jewish people. Hence it is dear that they lived long before Thales and 
much longer before Aristotle, who lived during the time of Alexander. These poets dealt to 
some extent with the nature of things by means of certain figurative representations in myths. 
For they said that Oceanus [i.e., the ocean], where the greatest aggregation of waters is found, 
and Tethys, which is the name they gave to the goddess of the waters, are the parents of 
generation, implying by this, under the form of a myth, that water is the principle of 
generation. 

84. They cloaked this view in another fabulous story, saying that the oath or vow of the gods 
was by a certain body of water, which the poets call Styx and describe as an underground 
swamp. And when they said that the gods swore by water, they implied that water was nobler 
than the gods themselves, because an oath or vow is taken on what is most honorable. Now 
that which is prior is more honorable; for the perfect is prior absolutely to the imperfect, both 


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in nature and in time, although in a particular being imperfection is prior temporally to 
perfection. Hence, from this it is evident that they thought that water is prior to the gods 
themselves, whom they thought to be celestial bodies. And since these earliest thinkers said 
that water is the principle of things, if there was any opinion about natural bodies prior to 
theirs, we do not know what it was. Thus what Thales is said to have thought about the first 
cause of things is now clear. 

85. A certain philosopher named Hippo was not credited with adding anything to those 
mentioned because of the imperfection of his knowledge or understanding. Hence, in The 
Soul, Hippo is placed among the ruder [thinkers] ; for in that work it is stated that Hippo, 
basing his argument on the seeds of things, as was said here of Thales, held water to be the 
soul and principle of things. Hence it is clear that he adds nothing to Thales' view. Or the 
statement can mean that, since he spoke imperfectly, he did not make himself worthy to have 
his doctrine included here with the others. 

86. Anaxinienes and Diogenes (41). 

Here he gives the opinions of those who held that air is the principle of things, namely, 
Diogenes and Anaximenes, who held that air is naturally prior to water and is the principle of 
all simple bodies, i.e., of the four elements, and thus of all other things. Anaximenes is the 
third philosopher after Thales and the disciple of Anaximander, who was the disciple of 
Thales; and Diogenes is said to have been the disciple of Anaximenes. Yet there is this 
difference between the opinion of Diogenes and that of Anaximenes: Artaximenes held that 
air is the principle of things in an absolute sense, whereas Diogenes said that air could be the 
principle of things only if it possessed a divine nature. From this comes the opinion which is 
touched on in The Soul, Book I. Now the reason why he held that air is the principle of things 
could be taken from the process of respiration, by which the life of animals is conserved, and 
because the processes whereby things are generated and corrupted seem to be modified as a 
result of changes in the air. 

87. Hippasus of Metopontium (42). 

Here he states that the two philosophers, Hippasus and Heraclitus, held that fire is the 
material principle of things. And they could have been influenced by its subtileness, as is said 
below. 

88. Empedocles (43). 

Here he gives the opinions of those who posited many material principles. First, he gives the 
opinion of Empedocles, who held that there are a limited number of such principles; and 
second 90), that of Anaxagoras, who held that there are an infinite number ("Anaxagoras"). 

First (43), he gives Empedocles' opinion regarding the three elements mentioned above, 
water, air, and fire, which he says are the principles of things, adding to them a fourth, earth. 

89. Second, he gives Empedocles' opinion about the permanence of these elements; for, like 
those who hold that there is one material cause, he holds that these elements always remain 
and are neither generated nor corrupted. However, he said that other things are generated 
from and dissolved into these elements according as a greater or smaller number of them are 
combined or separated out, i.e., inasmuch as these four are united by the process of 
combination and lose their unity by the process of separation. 


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90. Anaxagoras (44). 

Here he gives the opinion of Anaxagoras, who was the other disciple of Anaximenes and the 
classmate of Diogenes. A native of Clazomenae, he was prior to Empedocles in years but 
later in his activity or work, either because he began to philosophize later, or because his 
explanation of the number of principles is less satisfactory than that of Empedocles. For he 
said that there are an infinite number of material principles, whereas it is better to take a 
limited and smaller number, as Empedocles did, as is stated in Book I of the Physics. For 
Anaxagoras not only said that fire, water, and the other elements are the principles of things, 
as Empedocles did, but also claimed that all things having like parts, such as flesh, bones, 
marrow and so forth, whose smallest parts are infinite in number, are the principles of things. 
For he claimed that in each being there are an infinite number of parts of each type of thing, 
because he found that in the case of inferior things one of these can be generated from 
another. He said, in fact, that things could be generated only by being separated out from a 
mixture, as Aristotle has explained more fully in the Physics, Book I. 

91. Second, Anaxagoras also agrees with Empedocles on this point, namely, that things are 
generated and corrupted only insofar as the parts of these infinite principles are combined or 
separated out, and that if this were not the case nothing would be generated or corrupted. But 
he said that the infinite number of principles of this kind, from which the substances of things 
are produced, always remain in being. 

92. From the opinions of these philosophers, then, Aristotle concludes that the only cause 
which these men recognized was the one which belongs to the class of material cause. 


LESSON 5 

Opinions about the Efficient Cause 

ARISTOTLE'S TEXT Chapters 3 & 4: 984a 16-984b 32 

45. But as men proceeded in this way, reality itself again opened up a path and forced them to 
make investigations. For if every process of generation and corruption is from some one thing 
or more than one, why does this occur, and what is the cause? For certainly the subject itself 
does not cause itself to change. I mean, for example, that neither wood nor bronze is the cause 
of the change undergone by either one of them; for wood does not produce a bed, or bronze a 
statue, but something else is the cause of the change. But to seek this is to seek another 
principle, as if one were to say that from which the beginning of motion comes. 

46. Now in general those who have taken such a course from the very beginning, and who 
said that the subject is one, created no difficulty for themselves when they said that 
everything is one. [But some of those who say that it is one ], being baffled, so to speak, by 
this question, say that this [one subject] and the whole of nature is immobile not only with 
respect to generation and 

corruption (for this is an ancient opinion and one which all men confess to be true), but also 
with respect to every other change. This opinion is peculiar to them. Hence, of those who said 


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that the [universe] itself is one, it occurred to none of them to conceive of such a cause, 
except perhaps Parmenides, and to him only insofar as he claims that there is not one cause 
but also in a sense two causes. But for those who make the elements of things many, such as 
the hot and cold, or fire and earth, a better explanation is possible, because they use fire as if 
it were a material principle which is active in nature, but water and earth and the like they use 
in the opposite way. 

47. After these men and such principles, as if they were insufficient to generate the natures of 
existing things, men were again compelled (as we said [45]) by the truth itself to seek for the 
next principle. For perhaps it is unlikely that either fire or earth or anything else of this kind 
should be the cause of the good dispositions of things which are or come to be; nor was it 
consistent that they should think this to be the case. Nor again would it be right to attribute so 
important a matter to chance occurrence and fortune. 

48. And when someone said that there is one intellect present in nature as in animals, and that 
this is the cause of the world and the arrangement of the whole, he seemed to atone for the 
untenable statements made by his predecessors. 

We know that Anaxagoras expressed these views, although Hermotimus of Clazomenae was 
the first to speak of such a cause. Those, therefore, who held these opinions likewise posited a 
principle in existing things which is the cause of their goodness, and that sort of cause which 
is the source of motion in the world. 

Chapter 4 

49. Now someone might have suspected that Hesiod was the first to have investigated this 
sort of cause, or anyone else who held that love or desire is a principle in existing things, as 
Parmenides did. For in the place where he attempts to explain the generation of the universe, 
he says that "Love, the first of all the gods, was made." And Hesiod says that "The first of all 
things to be made was chaos, then broad earth, and love, who is pre-eminent among the 
immortals" — as though there must be in the world some cause which moves things and brings 
them together. How one must arrange these thinkers in sequence will be decided later on. 

COMMENTARY 

93. Having given the philosophers opinions about the material cause, Aristotle now gives 
their opinions about the efficient cause, which is the source of motion. This is divided into 
two parts. First, he gives the opinion of those who assigned without qualification a cause of 
motion and generation. Second (97), he examines the opinion of those who posited an 
efficient cause, which is also the principle of good and evil in the world ("After these men"). 

In regard to the first he does two things. First, he gives the reasoning which compelled them 
to posit an efficient cause. Second (94), he shows the different positions which different men 
have held regarding this ("Now in general"). 

He says (45), then, that some philosophers have proceeded in this way in positing a material 
cause, but that the very nature of reality clearly provided them with a course for 
understanding or discovering the truth, and compelled them to investigate a problem which 
led them to the efficient cause. This problem is as follows: no thing or subject changes itself; 
for example, wood does not change itself so that a bed comes from it, nor does bronze cause 
itself to be changed in such a way that a statue comes from it; but there must be some other 


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principle which causes the change they undergo, and this is the artist. But those who posited a 
material cause, whether one or more than one, said that the generation and corruption of 
things come from this cause as a subject. Therefore there must be some other cause of change, 
and to seek this is to seek another class of principle and cause, which is called the source of 
motion. 

94. Now in general (46). 

He shows here that the philosophers have adopted three positions with respect to the 
foregoing issue. For those who adopted this course from the very beginning, and said that 
there is one material cause, were not greatly concerned with the solution of this problem. For 
they were content with their view of matter and neglected the cause of motion altogether. 

95. But others, who said that all things are one, being defeated as it were by this issue, as they 
were unable to go so far as to assign a cause of motion, denied motion altogether. Hence they 
said that the whole universe is one immobile being. In this respect they differed from the first 
philosophers of nature, who said that one cause is the substance of all things although it is 
moved by rarefaction and condensation, so that in this way many things come to be in some 
measure from one principle. However, they did not say that this principle is subject to 
generation and corruption in an absolute sense. For the view that nothing was generated or 
corrupted without qualification is an ancient one admitted by all of them, as is clear from 
what was said above (75). But it was peculiar to these later thinkers to say that the whole of 
reality is one immobile being, devoid of every kind of motion. These men were Parmenides 
and Melissus, as will be explained below (138). Hence it is evident that it was impossible for 
those who said that the whole is one immobile being to conceive of "such a cause," i.e., a 
cause of motion. For, by the very fact that they did away with motion, they sought in vain for 
a cause of motion. An exception was Parmenides; for even though he held that there is only 
one thing according to reason, he held that there are many things according to the senses, as 
will be stated below (101). Hence, inasmuch as Parmenides held that there are many things, it 
was in keeping with his position to hold that there are many causes, one of which would be a 
mover and the others something moved. For just as he held that there are many things 
according to the senses, in a similar way it was necessary for him to hold that there is motion 
according to the senses, because a plurality of things can be understood to be produced from 
one subject only by some kind of motion. 

96. Third, there were those who, in making the substances of things many, assented to the 
aforesaid reasoning by positing a cause of motion. For they maintained that the hot or the 
cold, i.e., fire or earth, are causes; and of these they used fire as having a mobile, i.e., an 
active, nature, but water, earth and air they used in the opposite way, i.e., as having a passive 
nature. Thus fire was a sort of efficient cause, but the others a sort of material cause. 

97. After these men (47). 

Here he gives the opinion of those who posited an efficient cause, not only as a principle of 
motion, but also as a principle of good and evil in things. In regard to this he does two things. 
First, he expounds their views. Second (107), he shows in what respect they failed in 
assigning the causes of things ("These thinkers"). 

In regard to the first he does two things. First, he gives the reasons for their position by which 
they were induced to posit another cause besides the foregoing one. Second (100), he shows 
how they posited this kind of cause in different ways ("And when someone"). 


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He says first, then, that after the foregoing philosophers who held that there is only one 
material cause, or many bodies, one of which was active and the others passive, and after the 
other first principles given by them, men were again compelled by the truth itself ' "as we 
have said," i.e., as was stated above (93), to seek the "next" principle, i.e., the one which 
naturally follows the foregoing one, namely, the cause of good, which is really the final 
cause, although it was held by them only incidentally, as will be see below (177). For they 
held that there is a cause of goodness in things only after the manner of an efficient cause. 
They were compelled to do this because the foregoing principles were not sufficient to 
account for the generation of the natural world, in which some things are found to be well 
disposed . The fact that bodies are conserved in their proper places and are corrupted outside 
of them proves this; and so do the benefits resulting from the parts of animals, which are 
found to be disposed in this manner according as this is in keeping with an animal's good 
state of being. 

98. But neither fire nor earth nor any such bodies were held to be adequate causes of this kind 
of good disposition or state of being which some things already have but others acquire by 
some kind of production. For these bodies act in one definite way according to the necessity 
of their proper forms, as fire heats things and tends upward, and water cools things and tends 
downward. But the aforesaid benefits and good states of being of things must have a cause 
which is not limited to one effect only, since the parts of different animals are found to be 
disposed in different ways, and in each one insofar as it is in keeping with its nature. 

99. Hence, it is not reasonable that fire or earth or the like should be the cause of the aforesaid 
good state of being which things have, nor was it reasonable that these men should have 
thought this to be the case. Nor again would it be reasonable to say that these things are 
chance occurrences, i.e., that they are accidental or come about by chance, and that their 
causality is changed only fortuitously; although some of these thinkers had said this, as 
Empedocles and all those who posited a material cause, as is evident in Book II of the 
Physics. However, this is also seen to be false by reason of the fact that good dispositions of 
this kind are found either always or for the most part, whereas things that come about by 
chance or fortune do not occur always or for the most part but seldom. For this reason, then, it 
was necessary to discover besides the four elements some other principle which would 
account for the good dispositions of things. Another text has "Nor would it be right that these 
should be attributed to chance occurrence and fortune," but this means the same as the above. 

OPINIONS ON EFFICIENT CAUSE: intellect or love 

100. And when someone said (48). 

Here he gives in detail the opinions about the aforesaid principle. First, he gives the opinions 
of those who held that there is one [efficient] cause; and second (104), the opinions of those 
who held that there are two such causes ("But since there would seem"). 

In regard to the first he does two things. First, he gives the views of those who held that the 
first efficient cause is an intellect; and second (101), the opinions of those who held that it is 
love ("Now someone might"). 

He says, then, that after the foregoing doctrine someone appeared who said that there is an 
intellect present in nature at large, just as there is in animals, and that this is the cause of the 
world and the order of the whole, i.e., of the universe, in which order the good of the entire 
universe and that of every single part consists. And this man atoned for the first philosophers 


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by reducing to pure truth those who said unreasonable things and did not mention this kind of 

cause. Now Anaxagoras clearly stated this doctrine, although another philosopher 

— Hermotimus of Clazomenae — first gave him the idea of proposing this opinion. Hence it is 

evident that those who held this opinion claimed at the same time that the principle by which 

things are well disposed and the one which is the source of motion in things, are one and the 

same. 

101. Now someone might (49). 

Here he gives the opinion of those who claimed that love is the first principle, although they 
did not hold this very explicitly or clearly. Accordingly, he says that some suspected that 
Hesiod had sought for such a principle to account for the good disposition of things, or 
anyone else who posited love or desire in nature. For when Parmenides attempted to explain 
the generation of the universe, he said that in the establishing of the universe "Love, the first 
of all the gods, was made." Nor is this opposed to his doctrine that there is one immobile 
being, of which Aristotle speaks here; because this man held that there are many things 
according to the senses, although there is only one thing according to reason, as was stated 
above and will be stated below. Moreover, he called the celestial bodies, or perhaps certain 
separate substances, gods. 

102. But Hesiod said that first of all there was chaos, and then broad earth was made, to be 
the receptacle of everything else; for it is evident that the receptacle [or void] and place are 
principles, as is stated in Book IV of the Physics. And he also held that love, which instructs 
all the immortals, is a principle of things. He did this because the communication of goodness 
seems to spring from love, for a good deed is a sign and effect of love. Hence, since 
corruptible things derive their being and every good disposition from immortal beings of this 
kind, this must be attributed to the love of the immortals. Furthermore, he held that the 
immortals are either the celestial bodies themselves, or material principles themselves. Thus 
he posited chaos and love as though there had to be in existing things not only a material 
cause of their motions, but also an efficient cause which moves and unites them, which seems 
to be the office of love. For love moves us to act, because it is the source of all the emotions, 
since fear, sadness and hope proceed only from love. That love unites things is clear from 
this, that love itself is a certain union between the lover and the thing loved, seeing that the 
lover regards the beloved as himself. This man Hesiod is to be numbered among the poets 
who lived before the time of the philosophers. 

103. Now, as to which one of these thinkers is prior, i.e., more competent in knowledge, 
whether the one who said that love is the first principle, or the one who said hat intellect is, 
can be decided later on, that is, where God is discussed. He calls this decision an 
arrangement, because the degree of excellence belonging to each man is allotted to him in this 
way. Another translation states this more clearly: "Therefore, in what order it is fitting to go 
over these thinkers, and who in this order is prior, can be decided later on." 


LESSON 6 

Love and Hate as Efficient Causes of Good and Evil 
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ARISTOTLE'S TEXT Chapter 4: 984b 32-985b 4 

50. But since there would seem to be in nature things which are contrary to those that are 
good, and not only order and good but also disorder and what is base, and evil things more 
numerous than good ones, and base things more numerous than noble ones, for this reason 
another thinker introduced love and strife as causes, each of its own type of effects. For if 
anyone grasps what Empedocles said, taking it according to its meaning rather than according 
to its faltering expression, he will find that love is the cause of things which come to be by 
aggregation, and strife the cause of evil things. Hence, if anyone were to say that Empedocles, 
in a sense, both said and was the first to say that good and evil are princip es, he would 
perhaps speak correctly, i.e., if the cause of all good things is good and that of all evil things 
is evil. 

51. These thinkers, then, as we have said, to this extent have touched on two of the causes 
which we established in the Physics, — matter and the source of motion — though only 
obscurely and with no clarity, much as untrained men conduct themselves in battle. For the 
latter, though encircled, often deal telling blows, but without science. In the same way these 
thinkers do not seem to be aware of what they are saying. For it seems that they almost never 
make use of the causes except to a small degree. 

52. Anaxagoras uses "intellect" in an artificial way in generating the world. For when he is in 
difficulty as to what is necessarily the cause of something, he drags in this intellect; but in 
other cases he makes everything but intellect the cause of what comes to be. 

53. Empedocles, it is true, makes greater use of causes than Anaxagoras, though not 
sufficiently; nor does one find in his use of them what he professed. In many places he argues 
that love separates things, and that strife brings them together. For when being itself is 
separated into its elements by strife, then fire and each of the other elements are brought 
together into a unity. But when they are united by love, the particles must again be separated 
out from each element. 

54. In contrast to the first philosophers, then, Empedocles was the first to introduce this cause, 
dividing it in such a way as to make the source of motion not a single principle but different 
and contrary ones. Moreover, he was the first to claim that the elements, which are said to 
belong to the class of matter, are four in number, although he does not use them as four but as 
two, taking fire by itself alone, and its opposites — earth, air, and water — as a single nature 
(46). 

But anyone may see this by studying his basic sayings. This philosopher, then, as we have 
said, has spoken in this way about the principles of things and their number. 

COMMENTARY 

104. Here Aristotle gives the opinion of those who posited contrariety in beings of this kind, 
and the reason which moved them, which is as follows. There would seem to be in nature 
things which are contrary to those that are good, because in nature one finds not only things 
which are ordered and good, but sometimes things which are disordered and base. Now it 
cannot be said that evil things have no cause but happen by chance, because evil things are 
more numerous than good ones, and base things more numerous than those which are 
unqualifiedly noble. But those things which come to be by chance without a definite cause do 
not occur for the most part but in the smaller number of cases. Hence, since contrary effects 


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have contrary causes, it was necessary to hold as a cause of things not only love, from which 
the order and good in things originate, but also hate, which is the source of disorder and 
baseness or evil in things, so that in this way particular instances of evil and good have their 
own type of causes. 

105. That this was the reason which moved Empedocles is evident if anyone grasps what he 
says, taking his statement according to its meaning rather than according to the words which 
he used imperfectly and, as it were, in a faltering way. For he said that it is the office of love 
to bring the elements together, and of hate to separate them. But since the generation of things 
is a result of the coming together [of the elements], by reason of which there is being and 
good in things, and their corruption a result of the separation [of the elements], which is the 
way to non-being and evil, it is now evident that he wanted love to be the cause of things 
which come to be by aggregation, i.e., of good things, and hate the cause of evil things. Thus 
if one were to say that Empedocles was the first to maintain that good and evil are principles, 
he would perhaps speak correctly. 

106. That is to say, this would follow if Empedocles did hold that good is the cause of all 
good things, and evil the cause of all evil things. For it is evident that he posited evil as the 
cause of some evil things, namely, of corruption, and good as the cause of some good things, 
namely, of generation. But because it would not follow that all good things would be caused 
by friendship or all evil things by hate, since the parts of the world would be differentiated by 
hate and fused together by friendship, therefore he did not always hold that good is the cause 
of good things, and evil the cause of evil things. 

107. These thinkers (51). 

Here he shows that in giving these causes the philosophers treated them inadequately. First, 
he mentions them in a general way. Second (108), he treats each one individually 
("Anaxagoras"). 

He says first, then, that these philosophers — Anaxagoras and Empedocles — arrived at a 
doctrine of two of the causes which have been established in the Physics, namely, matter and 
the cause of motion, although they treated these obscurely and with no clarity, because they 
did not explain that those principles which they held to be the causes of things could be 
reduced to these classes of causes. But insofar as they posited two of these causes, they may 
be likened to untrained warriors who, ttiough encircled by the enemy, sometimes strike good 
blows, not by art but by chance. This is evident from the fact that, even though they happen to 
do this sometimes, this does not occur always or for the most part. In like manner, too, these 
philosophers were not accustomed to express themselves accurately, nor was it their custom 
to speak with awareness, i.e., as men who know. Hence another translation has, "But these 
men neither have science, nor are they to be compared with men who realize what they are 
saying." This is shown by the fact that, although they had proposed these causes, they hardly 
ever used them, because they employed them in few instances. Hence it seems that they 
introduced them not as a result of art but by accident, because they were moved to, do so by 
necessity. 

108. Anaxagoras (52). 

Here he shows in what particular respect the view of each is unsatisfactory. First, he speaks of 
Anaxagoras; and second (109), of Empedocles ("Empedocles"). 


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He says first, then, that Anaxagoras uses "intellect" to generate the world, and in so doing he 
seems to speak of it in an artificial way. For when he inquires about the causes of the world's 
generation, he drags it in of necessity, i.e., he invents this intelligence only because he is 
unable to attribute the generation of the world to any other cause which would differentiate 
things except to one which is essentially distinct and unmixed, and intellect is a thing of this 
kind. But in all other cases he draws his causes from any other source rather than intellect, for 
example, in the case of the particular natures of things. 

109. Empedocles (53). 

Here he shows in what respect Empedocles' doctrine is inadequate; and in regard to this he 
does two things. First, he shows in what respect Empedocles' doctrine is inadequate. Second 
(1 1 1), he explains what Empedocles himself held in contrast to the other philosophers ("In 
contrast" ) 

He says, first (53), that Empedocles, in dealing with the particular natures of things, "makes 
greater use of the causes" posited by him (the four elements, and love and hate) than 
Anaxagoras did, because he reduced the generation and corruption of particular things to 
these causes, and not to intelligence as Anaxagoras did. But Empedocles failed in two ways. 

First, he failed because he does not treat causes of this kind adequately enough; for he uses 
things which are not self-evident as though they were self-evident axioms, as is stated in the 
Physics, Book W that is, insofar as he assumed that they are self-evident, because at one 
definite time strife has dominion over the elements and at another, love. 

110. Second, he failed because in the matters which he investigates, one does not find what he 
has professed, i.e., what he held as a principle, namely, that love combines things and that 
strife separates them, because in many places love must on the contrary "separate" or divide 
things, and strife "bring them together," i.e., unite them. For when the universe itself "is 
separated out," i.e., divided into its parts, by hate, as occurs when the world is generated, all 
particles of fire are then combined into one whole, and so also are the individual particles of 
the other elements "brought together," i.e., joined to each other. Hence, strife not only 
separates the particles of fire from those of air, but also brings together the particles of fire. 
But, on the other hand, when the elements come together through love, which occurs when 
the universe is destroyed the particles of fire must then be separated from each other, and so 
also must the particles of the other elements. For fire can be mixed with air only if the 
particles of fire are separated from each other; and the same is true of the particles of air only 
if these elements penetrate one another, so that love not only unites unlike things but also 
separates like things, according to what follows from his position. 

111. In contrast (54). 

Here he shows in what respect Empedocles' own doctrine differs from that of the other 
philosophers. He says that Empedocles maintained two things in contrast to the others. First, 
he divided the cause which is the source of motion into two contrary parts. Second, he held 
the material cause to be constituted of four elements — not that he uses the four elements as 
four, but rather as two, because he contrasts fire with the other three, saying that fire is active 
in nature and the others passive in nature. Anyone can gather this from the elements of things 
treated by him, or from his "basic sayings" in the sense of the rudiments of the doctrine which 
he propounded. Another version reads "from his verses," because he is said to have written 
his philosophy in meters. And still another version, which says "from his statements," agrees 


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with this. As has been stated, then, this philosopher was the first to stipulate in this way that 
the principles of things are so many in number, namely, four, and to speak of those which 
have been mentioned. 


LESSON 7 

The Views of the Atomists and the Pythagoreans 
ARISTOTLE'S TEXT Chapters 4 & 5: 985b 4-986a 13 

55. Leucippus and his colleague Democritus say that the elements of things are the full and 
the void, calling the one being and the other non-being. For this reason they say that the full 
or solid is being, and the void, non-being. For this reason too they say that being no more is 
than non-being, because the void no more is than body; and they hold that these are the 
material causes of things. 

56. And just as those who make the underlying substance one generate other things from this 
by means of its attributes, holding that rarity and density are the principles of these attributes, 
in the same way these men say that the differences [of the atoms] are the causes of other 
things. These differences, they say, are three: shape, arrangement, and position. For they 
claim that what exists differs only by rhythm, inter-contact, and turning; and of these rhythm 
means shape, inter-contact arrangement, and turning position. For A differs from N in shape, 
and Z from N in position. But with regard to motion, from whence it comes or how it is 
present in things, these men carelessly dismissed this question as the other thinkers did. As 
we have said before, then, these two types of causes seem to have been investigated to this 
extent by the first thinkers. 

Chapter 5 

57. But during the time of these and prior to them, lived the group called the Pythagoreans 
who dealt with mathematics and were the first to develop it; and having been brought up in 
these sciences, they thought that their principles were the principles of all things. But since 
among these principles numbers are naturally first, they thought they saw in numbers, more 
than in fire and earth, many resemblances to things which are and come to be, because 
[according to them] this attribute of numbers is justice, another is soul and mind, and still 
another is opportunity. The case is the same, so to speak, with every other thing. 

58. Moreover, since they considered the attributes and ratios of harmonies in terms of 
numbers, and since other things in their whole nature seemed to be likened to numbers, and 
since numbers are the first things in the whole of nature, they thought that the elements of 
numbers are the elements of all things, and that the whole heaven is a harmony and number. 
And whatever they had revealed in the case of numbers and harmonies [which they could] 
show [to be in agreement] with the motions and parts of the heavens, and its whole 
arrangement, they collected and adapted to these. And if anything was lacking anywhere, they 
called it in in order that their undertaking might be complete. I mean that since the number ten 
seems to be the perfect number and to comprise the whole nature of numbers, they said that 
the bodies which move in the heavens are ten in number; but as only nine are observable they 
therefore invented a tenth, the counter-earth. These things have been dealt with more exactly 

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in another work [De Coelo, II, 13]. 

COMMENTARY 

112. Here he begins to give the positions of those who held strange and obscure views about 
the principles of things. First, he gives the position of those who held that there are many 
principles of things; and second (134) the position of those who held that there is only one 
being ("But there are some"). 

In regard to the first he does two things. First, he gives the opinion of Leucippus and 
Democritus, who held that the principles of things are corporeal. Second (119), he gives the 
opinion of the Pythagoreans, who held that the principles of things are incorporeal entities 
("But during the time"). 

In regard to the first he does two things. First, he gives the opinion of Democritus and 
Leucippus about the material cause of things; and second (115), their opinion about the cause 
of diversity, that is, how matter is differentiated into many things. In this discussion the cause 
of the generation and corruption of things also becomes evident; and this is a point on which 
these men agreed with the ancient philosophers ("And just as those who"). He says, then, that 
two philosophers, Democritus and Leucippus, who are called friends because they followed 
each other in all things, held that the principles of things are the full and the void or empty, of 
which the full is being, and the void or empty, non-being. 

113. Now in order to clarify this opinion we must recall what the Philosopher says in Book I 
of Generation, where he treats it more fully. For certain philosophers had held that everything 
is one continuous immobile being, because it seems that there cannot be motion without a 
void, or any distinction between things, as they said. And though they could not comprehend 
the privation of continuity, by reason of which bodies must be understood to be differentiated, 
except by means of a void, they claimed that the void existed in no way. Democritus, who 
came after them, and who agreed with their reasoning but was unable to exclude diversity and 
motion from things, held that the void existed, and that all bodies are composed of certain 
indivisible bodies [i.e., the atoms]. He did this because it seemed to him that no reason could 
be given why the whole of being should be divided in one part rather than another. And lest 
he should hold that the whole of being is continuous, he therefore chose to maintain that this 
whole is divided everywhere and in its entirety; and this could not be the case if anything 
divisible remained undivided. And according to him indivisible bodies of this kind can neither 
exist nor be joined together except by means of the void. For if the void did not come 
between any two of them, one continuous whole would result from the two; which he did not 
hold for the above reason. Hence he said that the continuous quantity of each body is 
constituted both of those indivisible bodies filling indivisible spaces and of certain empty 
spaces, which he called pores, coming between these indivisible bodies. 

114. And since the void is non-being and the full is being, it is evident from this that he did 
not hold that a thing was constituted by being rather than non-being, because the [indivisible] 
bodies did not constitute things more than the void, or the void more than bodies; but he said 
that a body is composed at once of these two things, as is clear in the text. Hence he held that 
these two things are the causes of beings as their matter. 

115. And just as those (56). 


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Here he shows in what respect these philosophers agreed with the ancients who claimed that 
there is only one matter. He indicates agreement in two respects. 

First, just as the ancient philosophers held that there is one matter, and from that one matter 
generated something else according to the different attributes of matter (i.e., the rare and 
dense, which they accepted as the principles of all other attributes), in a similar way these 
philosophers — Democritus and Leucippus — said that there were different causes of different 
things (namely, of the bodies composed of these indivisible bodies), i.e., that different beings 
were produced as a result of certain differences of these indivisible bodies and their pores. 

116. Now they said that these differences are, first, differences in shape, which is noted from 
this that things are angular, circular or square; second, differences in arrangement, i.e., insofar 
as the indivisible bodies are prior or subsequent; and, third, differences in position, i.e., 
insofar as these bodies are in front or behind, right or left, or above and below. Hence they 
said that one being differs from another "either by rhythm," which is shape, "or by 
inter-contact," which is arrangement, "or by turning," which is position. 

117. He illustrates this by using the letters of the Greek alphabet, which differ from each other 
in shape just as in our alphabet one letter also differs from another; for A differs from N in 
shape. Again, AN differs from NA in arrangement, because one letter is placed before the 
other. And one letter also differs from another in position, as Z from IN, just as in our 
language we also see that semivowels cannot stand after liquids preceded by mutes in the 
same syllable. Therefore, just as tragedy and comedy come from the same letters as a result of 
the letters being disposed in different ways because of this threefold difference, in a similar 
fashion different species of things are produced from the same indivisible bodies as a result of 
the latter being disposed in different ways. 

118. The second respect in which these philosophers agreed with the ancients is this: just as 
the ancient philosophers neglected to posit a cause which accounts for motion in things, so 
also did these men, although they would say that these indivisible bodies are capable of 
self-motion. Thus it is evident that these philosophers mentioned only two of the causes, i.e., 
all of them spoke of the material cause) and some of the efficient cause. 

119. But during the time of these (57). 

Here he gives the opinions of the Pythagoreans, who held that numbers are the substances of 
things. In regard to this he does two things. First, he gives their opinions about the substance 
of things; and second (124), their opinions about the principles of things ("But the reason"). 

In regard to the first he gives two reasons by which they were led to assert that numbers are 
the substances of things. He gives the second reason (121) where he says "Moreover, since 
they considered." 

He says that the Pythagoreans were philosophers who lived "during the time of these," i.e., 
they were contemporaries of some of the foregoing philosophers; "and prior to them," 
because they preceded some of them. Now it must be understood that there were two groups 
of philosophers. One group was called the Ionians, who inhabited the land which is now 
called Greece. This group originated with Thales, as was pointed out above (77). The other 
group of philosophers were the Italians, who lived in that part of Italy which was once called 
Greater Greece and is now called Apulia and Calabria. The leader of these philosophers was 
Pythagoras, a native of Samos, so called from a certain city of Calabria. These two groups of 


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philosophers lived at the same time, and this is why he says that they lived "During the time 
of these and prior to them." 

120. These Italian philosophers, also called Pythagoreans, were the first to develop certain 
mathematical entities, so that they said that these are the substances and principles of sensible 
things. He says that they were "the first" because the Platonists were their successors. They 
were moved to bring in mathematics because they were brought up in the study of these 
sciences, and therefore they thought that the principles of mathematics are the principles of all 
existing things. For men are wont to judge about things in terms of what they already know. 
And since among mathematical entities numbers are first, these men therefore tried to see 
resemblances of natural things, both as regards their being and generation, in numbers rather 
than in the sensible elements — earth, water and the like. For just as the foregoing 
philosophers adapted the attributes of sensible things to those of natural things because of a 
certain resemblance which they bear to the properties of fire, water, and bodies of this kind, in 
a similar fashion these mathematicians adapted the properties of natural things to the 
attributes of numbers when they said that some one attribute of number is the cause of justice, 
another the cause of soul and intellect, and still another the cause of opportunity, and so on 
for other things. And in this way the attributes of numbers are understood to be the intelligible 
structures and principles of all things appearing in the sensible world, both in the realm of 
voluntary matters, signified by justice, and in that of the substantial forms of natural things, 
signified by soul and intellect, and in that of accidents, signified by opportunity. 

STRANGE AND OBSCURE VIEWS ABOUT THE PRINCIPLES OF THINGS 

Hidden principles: numbers 

121. Moreover, since they (58). 

Here he gives the second reason which motivated them. For they thought of the attributes of 
harmonies, musical consonants and their ratios, i.e., proportions, in terms of the nature of 
numbers. Hence, since harmonious sounds are certain sensible things, they attempted by the 
same reasoning to liken all other sensible things, both in their intelligible structure and in their 
whole nature, to numbers, so that numbers are the first things in the whole of nature. 

122. For this reason too they thought that the principles of numbers are the principles of all 
existing things, and they said that the whole heaven is merely a kind of nature and harmony of 
numbers, i.e., a kind of numerical proportion similar to the proportion found in harmonies. 
Hence, whatever they had "revealed," i.e., had shown, which they could adapt to numbers and 
harmonies, they also adapted both to the changes undergone by the heavens, as its motion, 
eclipses and the like; and to its parts, as the different orbs; and to the whole arrangement of 
the heavens, as the different stars and different figures in the constellations. 


LESSON 8 

The Pythagorean Doctrine about Contraries 
ARISTOTLE'S TEXT Chapter 5: 986a 13-986b 10 
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59. But the reason we have come [to examine these philosophers] is that we may also learn 
from them what they hold the principles of things to be, and how these principles fall under 
the causes already described. Now these men also seem to think that number is the principle 
of existing things both as their matter and as their attributes and states. According to them the 
elements of number are the even and odd, and of these the latter is limited and the former, 
unlimited. The unit is composed of both of these, since it is both even and odd, and number is 
derived from the unit. And number, as has been stated (58), constitutes the whole heaven. 

60. But other members of the same school say that the principles of things are ten in number, 
which they give as co-elements: the limited and unlimited, even and odd, one and many, right 
and left, masculine and feminine, rest and motion, straight and curved, light and darkness, 
good and evil, square and oblong. 

61. Alcmaeon of Croton seems to have formed his opinion in the same way, and either he 
derived the theory from them or they from him; for Alcmaeon (who had reached maturity 
when Pythagoras was an old man) expressed views similar to those of the Pythagoreans. For 
he says that many things in the realm of human affairs are in twos [i.e., pairs], calling them 
contrarieties, not distinguished as these men had distinguished them, but such as are taken at 
random, for example, white and black, sweet and bitter, good and evil, small and great. It is 
true that this philosopher threw out vague remarks about the other contrarieties, but the 
Pythagoreans have declared both what the contrarieties are and how many there are. 

62. From both of these, then, we can gather this much, that contraries are the principles of 
existing things; but how many they are and that they are these [determinate ones must be 
learned] from other thinkers. The way in which many principles can be brought together 
under the causes described is not clearly expressed by them, although they seem to allot their 
elements to the class of matter; for they say that substance is composed and moulded out of 
these as something inherent. From these remarks, then, it is possible to get an adequate 
understanding of the meaning of the ancient philosophers who said that the elements of things 
are many. 

COMMENTARY 

124. Here he states what the Pythagoreans had to say about the principles of things. In regard 
to this he does two things. First, he expounds their opinions about the principles of things; and 
second (132), he indicates to what class of cause the principles laid down by them are reduced 
("From both of these"). 

In regard to the first he gives three opinions. The second (127) begins at the words "But other 
members"; and the third (131), where he says "Alcmaeon of Croton." 

He says first (59), then, that the reason he came to examine the opinions of the Pythagoreans 
is that he might show from their opinions what the principles of things are and how the 
principles laid down by them fall under the causes given above. For the Pythagoreans seem to 
hold that number is the principle of existing things as matter, 1 and that the attributes of 
number are the attributes and states of existing things. By "attributes" we mean transient 
accidents, and by "states," permanent accidents. They also held that the attribute of any 
number according to which any number is said to be even is justice, because of the equality of 
division, since such a number is evenly divided into two parts right down to the unit. For 
example, the number eight is divided into two fours, the number four into two twos, and the 
number two into two units. And in a similar way they likened the other accidents of things to 


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the accidents of numbers. 

125. in fact, they said that the even and odd, which are the first differences of numbers, are 
the principles of num hers. And they said that even number is the principle of unlimitedness 
and odd number the principle of limitation, as is shown in the Physics, Book III, because in 
reality the unlimited seems to result chiefly from the division of the continuous. But an even 
number is capable of division; for an odd number includes within itself an even number plus a 
unit, and this makes it indivisible. He also proves this as followswhen odd numbers are added 
to each other successively, they always retain the figure of a square, whereas even numbers 
change their figure. For when the number three is added to the unit, which is the principle of 
numbers, the number four results, which is the first square [number], because 2x2 = 4. 
Again, when the number five, which is an odd number, is added to the number four, the 
number nine results, which is also a square number; and so on with the others. But if the 
number two, which is the first even number, is added to the number one, a triangular number 
results, i.e., the number three. And if the number four, which is the second even number, is 
added to the number three, there results a septangular number, i.e., the number seven. And 
when even numbers are added to each other successively in this way, they do not retain the 
same figure. This is why they attributed the unlimited to the even and the limited to the odd. 
And since limitedness pertains to form, to which active power belongs, they therefore said 
that even numbers are feminine, and odd numbers, masculine. 

126. From these two, namely, the even and odd, the limited and unlimited, they produced not 
only number but also the unit itself, i.e., unity. For unity is virtually both even and odd; 
because all differences of number are virtually contained in the unit; for all differences of 
number are reduced to the unit. Hence, in the list of odd numbers the unit is found to be the 
first. And the same is true in the list of even numbers, square numbers, and perfect numbers. 
This is also the case with the other differences of number, because even though the unit is not 
actually a number, it is still virtually all numbers. And just as the unit is said to be composed 
of the even and odd, in a similar way number is composed of units. In fact, [according to 
them], the heavens and all sensible things are composed of numbers. This was the sequence 
of principles which they gave. 

127. But other members (60). 

Here he gives another opinion which the Pythagoreans held about the principles of things. He 
says that among these same Pythagoreans there were some who claimed that there is not just 
one contrariety in principles, as the foregoing did, but ten principles, which are presented as 
co-elements, that is, by taking each of these principles with its co-principle, or contrary. The 
reason for this position was that they took not only the first principles but also the proximate 
principles attributed to each class of things. Hence, they posited first the limited and the 
unlimited, as did those who have just been mentioned; and subsequently the even and the odd, 
to which the limited and unlimited are attributed. And because the even and odd are the first 
principles of things, and numbers are first produced from them, they posited, third, a 
difference of numbers, namely, the one and the many, both of which are produced from the 
even and the odd. Again, because continuous quantities are composed of numbers, inasmuch 
as they understood numbers to have position (for according to them the point was merely the 
unit having position, and the line the number two having position), they therefore claimed 
next that the principles of positions are the right and left; for the right is found to be perfect 
and the left imperfect. Therefore the right is determined from the aspect of oddness, and the 
left from the aspect of evenness. But because natural bodies have both active and passive 
powers in addition to mathematical extensions, they therefore next maintained that masculine 


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and feminine are principles. For masculine pertains to active power, and feminine to passive 
power; and of these masculine pertains to odd number and feminine to even number, as has 
been stated (125). 

128. Now it is from active and passive power that motion and rest originate in the world; and 
of these motion is placed in the class of the unlimited and even, because it partakes of 
irregularity and otherness, and rest in the class of the unlimited and odd. Furthermore, the first 
differences of motions are the circular and straight, so that as a consequence of this the 
straight pertains to even number. Hence they said that the straight line is the number two; but 
that the curved or circular line, by reason of its uniformity, pertains to odd number, which 
retains its undividedness because of the form of unity. 

129. And they not only posited principles to account for the natural operations and motions of 
things, but also to account for the operations of living things. In fact, they held that light and 
darkness are principles of knowing, but that good and evil are principles of appetite. For light 
is a principle of knowing, whereas darkness is ascribed to ignorance; and good is that to 
which appetite tends, whereas evil is that from which it turns away. 

130. Again, [according to them] the difference of perfection and imperfection is found not 
only in natural things and in voluntary powers and motions, but also in continuous quantities 
and figures. These figures are understood to be something over and above the substances of 
continuous quantities, just as the powers responsible for motions and operations are 
something over and above the substances of natural bodies. Therefore with reference to this 
they held that what is quadrangular, i.e., the square and oblong, is a principle. Now a square is 
said to be a figure of four equal sides, whose four angles are right angles; and such a figure is 
produced by multiplying a line by itself. Therefore, since it is produced from the unit itself, it 
belongs to the class of odd number. But an oblong is defined as a figure whose angles are all 
right angles and whose opposite sides alone, not all sides, are equal to each other. Hence it is 
clear that, just as a square is produced by multiplying one line by itself, in a similar way an 
oblong is produced by multiplying one line by another. Hence it pertains to the class of even 
number, of which the first is the number two. 

131. Akmaeon of Croton (61). 

Here he gives the third opinion of the Pythagoreans, saying that Alcmaeon of Croton, so 
named from the city in which he was raised, seems to maintain somewhat the same view as 
that expressed by these Pythagoreans, namely, that many contraries are the principles of 
things. For either he derives the theory from the Pythagoreans, or they from him. That either 
of these might be true is clear from the fact that he was a contemporary of the Pythagoreans, 
granted that he began to philosophize when Pythagoras was an old man. But whichever 
happens to be true, he expressed views similar to those of the Pythagoreans. For he said that 
many of the things "in the realm of human affairs," i.e., many of the attributes of sensible 
things are arranged in pairs, understanding by pairs opposites which are contrary. Yet in this 
matter he differs from the foregoing philosophers, because the Pythagoreans said that 
determinate contraries are the principles of things. But he throws them in, as it were, without 
any order, holding that any of the contraries which he happened to think of are the principles 
of things, such as white and black, sweet and bitter, and so on. 


132. From both of these (62). 
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Here he gathers together from the above remarks what the Pythagoreans thought about the 
principles of things, and how the principles which they posited are reduced to some class of 
cause. 

He says, then, that from both of those mentioned above, namely, Alcmaeon and the 
Pythagoreans, it is possible to draw one common opinion, namely, that the principles of 
existing things are contraries; which was not expressed by the other thinkers. This must be 
understood with reference to the material cause. For Empedocles posited contrariety in the 
case of the efficient cause; and the ancient philosophers of nature posited contrary principles, 
such as rarity and density, although they attributed contrariety to form. But even though 
Empedocles held that the four elements are material principles, he still did not claim that they 
are the first material principles by reason of contrariety but because of their natures and 
substance. These men, however, attributed contrariety to matter. 

133. The nature of the contraries posited by these men is evident from the foregoing 
discussion. But how the aforesaid contrary principles posited by them can be "brought 
together under," i.e., reduced to, the types of causes described, is not clearly "expressed," i.e., 
distinctly stated, by them. Yet it seems that such principles are allotted to the class of material 
cause; for they say that the substance of things is composed and moulded out of these 
principles as something inherent, and this is the notion of a material cause. For matter is that 
from which a thing comes to be as something inherent. This is added to distinguish it from 
privation, from which something also comes to be but which is not inherent, as the musical is 
said to come from the non-musical. 


LESSON 9 

The Opinions of the Eleatics and Pythagoreans about the Causes of Things 
ARISTOTLE'S TEXT Chapter 5: 986b 10-987a 28 

63. But there are some [the Eleatics] who spoke of the whole as if it were a single nature, 
although the statements which they made are not all alike either with regard to their 
acceptableness or their conformity with nature. 

64. Therefore a consideration of these men pertains in no way to the present investigation of 
causes. For they do not, like certain of the philosophers [the early physicists] who supposed 
being to be one, still generate it from the one as matter; but they speak of this in another way. 
For the others assume motion when they generate this whole, whereas these thinkers say it is 
immobile. 

65. Yet their opinion is relevant to the present investigation to some extent; for Parmenides 
seems to touch on unity according to intelligible structure and Melissus on unity according to 
matter. This is why the former says that it is limited, and the latter that it is unlimited. 
Xenophanes, the first of those to speak of the one (for Parmenides is said to have been his 
disciple), made nothing clear, nor does he seem to have touched on either of these. But with 
regard to the whole heaven he says that the one is God. 


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66. As we have stated, then, these men must be dismissed for the purposes of the present 
inquiry. In fact, two of them — Xenophanes and Melissus — are to be disregarded altogether as 
being a little too rustic. Parmenides, however, seems to speak with more insight; for he 
thought that besides being there is only non-being, and this is nothing. This is why he thinks 
that being is necessarily one and nothing else. We have discussed this point more clearly in 
the Physics. But being compelled to follow the observed facts, and having assumed that what 
is one from the viewpoint of reason is many from the viewpoint of the senses, he postulates in 
turn two principles, i.e., two causes, the hot and cold, calling the one fire and the other earth; 
and of these he ranks the hot with being and the cold with non-being. 

67. From what has been said, then, and from the wise men who have already agreed with this 
reasoning, we have acquired these things. From the first philosophers we have learned that the 
principle of things is corporeal, because water and fire and the like are bodies; and from some 
we have learned that there is one corporeal principle, and from others, many; although both 
suppose that these belong to the class of matter. And from others we have learned that in 
addition to this cause there is the source from which motion begins, which some claim to be 
one and others two. Down to the Italian philosophers, then, and independent of them, others 
have spoken of these things in a more trivial way, except that, as we have said, they have used 
two kinds of causes, and one of these — the source of motion — some thinkers consider as one 
and others as two. 

68. Now the Pythagoreans have spoken of these two principles in the same way, but added 
this much, which is peculiar to them, that they did not think that the limited, unlimited and 
one are different natures, like fire or earth or anything else of this kind, but that the unlimited 
itself and the one itself are the substance of the things of which they are predicated. And this 
is why they considered number as the substance of all things. These thinkers, then have 
expres emselves thus with regard to these things, and they began to discuss and define the 
"what" itself of things, although they treated it far too simply. For they defined things 
superficially and thought that the substance of a thing is that to which a given definition first 
applies; just as if one supposed that double and two are the same because that to which the 
double first belongs is the number two. But perhaps "to be double" is not the same as "to be 
two"; and if they are not, then the one itself will be many. This, indeed, is the conclusion 
which they reached. From the first philosophers and others, then, this much can be learned. 

COMMENTARY 

Unitarians 

134. Here he gives the opinions of those philosophers who spoke of the whole universe as one 
being; and in regard to this he does two things. First, he gives the opinion which they held in 
common; and second (135), he shows how a consideration of this opinion is relevant to the 
present treatise, and how it is not ("Therefore a consideration"). 

He says, then, that there were certain philosophers, other than those just mentioned, who 
spoke "of the whole," i.e,, of the universe, as if it were of one nature, i.e., as if the whole 
universe were a single being or a single nature. However, not all maintained this position in 
the same way, as he will make clear below (138-49). Yet in the way in which they differ their 
statements are neither acceptable nor in conformity with nature. None of their statements are 
in conformity with nature, because they did away with motion in things. And none of them 
are acceptable, because they held an impossible position and used sophistical arguments, as is 
clear in Book I of the Physics. 


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135. Therefore a consideration (64). 

Here he shows how a consideration of this position pertains to the present investigation and 
how it does not. He shows, first, that it has no bearing on this investigation if we consider 
their position itself; and, second (137), that it does have a bearing on this investigation if the 
reasoning or method behind their position is considered ("Yet their opinion"). 

He says, then, that since these philosophers held that there is only one being, and a single 
thing cannot be its own cause, it is clear that they could not discover the causes. For the 
position that there is a plurality of things demands a diversity of causes in the world. Hence, a 
consideration of their statements is of no value for the purposes of the present study, which 
deals with causes. But the situation is different in the case of the ancient philosophers of 
nature, who held that there is only one being, and whose statements must be considered here. 
For they generated many things from that one principle as matter, and thus posited both cause 
and effect. But these men with whom we are now dealing speak of this in a different way. For 
they do not say that all things are one materially, so that all things are generated from one 
matter, but that all things are one in an absolute sense. 

136. The reason for this difference is that the ancient philosophers of nature added motion to 
the view of those who posited one being and one principle, and said that this one being is 
mobile; and therefore different things could be generated from that one principle by a certain 
kind of motion, i.e., by rarefaction and condensation. And they said that the whole universe 
with respect to the diversity found in its parts is generated in this way. Yet since they held 
that the only change affecting substance is accidental, as was stated above (75), the 
conclusion then followed that the whole universe is one thing substantially but many things 
accidentally. But these thinkers [i.e., the Eleatics], said that the one being which they posited 
is immobile in an absolute sense; and therefore a diversity of things could not be produced 
from that one being. For since this being is immobile they could not posit any plurality in the 
world, either substantial or accidental. 

137. Yet their opinion (65). 

Here he shows how their opinion is relevant to the present inquiry. First, he deals with all of 
these thinkers in general; and second (142), with Parmenides in particular. 

He says, first, that although they did away with diversity in the world, and consequently with 
causality, nevertheless their opinion is relevant to the present study to this extent, let us say: 
as regards the method by which they establish their position and the reason for their position. 

138. Parmenides, who was a member of this group, seems to touch on unity according to 
intelligible structure) i.e., according to form; for he argued as follows: besides being there is 
only non43eing, and non43eing is nothing. Therefore besides being there is nothing. But being 
is one. Therefore, besides the one there is nothing. 

In this argument he clearly considered the intelligible structure itself of being, which seems to 
be one, because nothing can be understood to be added to the concept of being by which it 
might be diversified. For whatever is added to being must be other than being. But anything 
such as this is nothing. Hence it does not seem that this can diversify being; just as we also 
see that differences added to a genus diversify it, even though these differences are outside 
the substance of that genus. For differences do not participate in a genus, as is stated in the 
Topics, Book IV, otherwise a genus would have the substance of a difference. And definitions 


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would be nonsense if when a genus is given the difference were added, granted that the genus 
were the substance of the difference, just as it would be nonsense if the species were added. 
Moreover a difference would not differ in any way from a species. But those things which are 
outside the substance of being must be non-being, and thus cannot diversify being. 

139. But they were mistaken in this matter, because they used being as if it were one in 
intelligible structure and in nature, like the nature of any genus. But this is impossible. For 
being is not a genus but is predicated of different things in many ways. Therefore in Book I of 
the Physics it is said that the statement "Being is one" is false. For being does not have one 
nature like one genus or one species. 

140. But Melissus considered being in terms of matter. For he argued that being is one by 
reason of the fact that being is not generated from something prior, and this characteristic 
pertains properly to matter, which is ungenerated. For he argued in this way: whatever is 
generated has a starting-point. But being is not generated and therefore does not have a 
starting-point. But whatever lacks a starting-point lacks an end and therefore is unlimited. 
And if it is unlimited, it is immobile, because what is unlimited has nothing outside itself by 
which it is moved. 

That being is not generated he proves thus. If being were generated, it would be generated 
either from being or from non-being. But it is not generated from non-being, because 
non-being is nothing and from nothing nothing comes. Nor is it generated from being, 
because then a thing would be before it came to be. Therefore it is not generated in any way. 

In this argument he obviously treats being as matter, because it is of the very nature of matter 
not to be generated from something prior. And since limitation pertains to form, and 
unlimitedness to matter, Melissus, who considered being under the aspect of matter, said that 
there is one unlimited being. But Parmenides, who considered being under the aspect of form, 
said that being is limited. Hence, insofar as being is considered under the aspect of form and 
matter, a study of these men is relevant to the present investigation; because matter and form 
are included among the causes. 

141. But Xenophanes, who was the first of those to say that everything is one (and therefore 
Parmenides was his disciple), did not explain by what reasoning he maintained that all things 
are one, either by arguing from the viewpoint of matter, or from that of form. Hence, with 
respect to neither nature, i.e., neither matter nor form, does he seem "to come up to these 
men," that is, to reach and equal them in their irrational manner of arguing. 

But concerning the whole heaven he says that the one is God. For the ancients said that the 
world itself is God. Hence, seeing that all parts of the universe are alike insofar as they are 
bodies, he came to think of them as if they were all one. And just as the foregoing 
philosophers held that beings are one by considering those things which pertain either to 
matter or to form, in a similar way these philosophers maintained this position regarding the 
composite itself. 

142. As we have stated (66). 

His aim here is to explain in a special way how the opinion of Parmenides pertains to the 
present investigation. He concludes from the foregoing that, since these men did away with 
(~) diversity in the world and therefore with (~) causality, all of them must be disregarded so 
far as the present study is concerned. Two of them — Xenophanes and Melissus — must be 


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disregarded altogether, because they are a little too "rustic," i.e., they proceeded with less 
accuracy. But Parmenides seems to have expressed his views "with more insight," i.e., with 
greater understanding. For he employs the following argument: besides being there is only 
non-being, and whatever is non-being "is thought to be nothing"; i.e., he considers it worthy 
to be nothing. Hence he thought that it necessarily followed that being is one, and that 
whatever is other than being is nothing. This argument has been treated more clearly in the 
Physics, Book I. 

143. But even though Parmenides was compelled by this argument to hold that all things are 
one, yet, because there appeared to the senses to be many things in reality, and because he 
was compelled to accept what appeared to the senses, it was his aim to make his position 
conform to both of these, i.e., to what is apprehended both by the senses and by reason. Hence 
he said that all things are one according to reason but many according to the senses. 

And inasmuch as he held that there is a plurality of things according to the senses, he was 
able to hold that there is in the world both cause and effect. Hence he posited two causes, 
namely, the hot and the cold, one of which he ascribed to fire, and the other to earth. And one 
of these — the hot or fire — seemed to pertain to the efficient cause, and the other — cold or 
earth — to the material cause. And lest his position should seem to contradict the conclusion of 
his own argument that whatever is besides being is nothing, he said that one of these 
causes — the hot — is being, and that the other cause — the one besides being, or the cold — is 
non-being, according to. both reason and the truth of the thing itself, and is a being only 
according to sensory perception. 

144. Now in this matter he comes very close to the truth; for the material principle, which he 
held to be earth, is not an actual being. 

And in a similar way, too, one of two contraries is a privation, as is said in Book I of the 
Physics. But privation does not belong to the intelligible constitution of being. Hence in a 
sense cold is the privation of heat, and thus is non-being. 

145. From what has been said (67). Here he summarizes the remarks which have been made 
about the doctrines of the ancient philosophers; and in regard to this he does two things. First, 
he summarizes the remarks made about the doctrines of the ancient philosophers of nature; 
and second (147), those made about the doctrines of the Pythagoreans, who introduced 
mathematics. 

Therefore from the above remarks he concludes, first, that from the foregoing philosophers, 
who adopted the same opinion, namely, that the material cause is the substance of things, and 
who were already beginning by the use of reason to know the causes of things by 
investigating them, we learn the causes which have been mentioned. For from the first 
philosophers it was learned that the principle of all things is corporeal. This is evident from 
the fact that water and the like, which are given as the principles of things, are bodies. 
However, they differed in this respect, that some, such as Thales, Diogenes and similar 
thinkers, claimed that there is only one corporeal principle, whereas others, such as 
Anaxagoras, Democritus and Leucippus, held that there are several corporeal principles. Yet 
both groups, i.e., both those who posited one principle and those who posited many, placed 
such corporeal principles in the class of material cause. And some of them not only posited a 
material cause but added to this the cause from which motion begins: some holding it to be 
one, as Anaxagoras did in positing intellect, and Parmenides, love, and others to be two, as 
Empedocles did in positing love and hate. 


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146. Hence, it is clear that these philosophers who lived down to the time of the Italians, or 
Pythagoreans, "and [were] independent of them," i.e., who had their own opinions about 
reality and were unaware of those of the Pythagoreans, spoke obscurely about the principles 
of things; for they did not designate to what class of cause such principles might be reduced. 
Yet they made use of two causes, i.e., the source from which motion begins and matter: some 
saying that the former — the source from which motion begins — is one, and others two; as has 
been pointed out (145). 

147. Now the Pythagoreans (68). 

Here he summarizes the opinions expressed by the Pythagoreans, both what they held in 
common with the foregoing philosophers, and what was peculiar to themselves. Now the 
opinion common to some of the foregoing philosophers and to the Pythagoreans was this that 
they posited, in a sense, two principles in the same way as the foregoing philosophers did. For 
Empedocles held that there are two contrary principles, one being the principle of good 
things, and the other the principle of evil things, and the Pythagoreans did the same thing, as 
is clear from the co-ordination of contrary principles which they posited. 

148. However, they did not do this in the same way; because Empedocles placed these 
contrary principles in the class of material cause, as was stated above (111), whereas the 
Pythagoreans added their own opinion to that of the other thinkers. The first thing that they 
added is this: they said that what I call the one, the limited and the unlimited are not (~) 
accidents of any other natures, such as fire or earth or the like, but claimed that what I call the 
one, the limited and the unlimited constitute the (+) substance of the same things of which 
they are predicated. From this they concluded that number, which is constituted of units, is 
the substance of all things. But while the other philosophers of nature posited the one, the 
limited and the unlimited, they nevertheless attributed these to another nature, as accidents are 
attributed to a subject, for example, to fire or water or something of this kind. 

149. The second addition which they made to the views of the other philosophers is this: they 
began to discuss and to define "the whatness itself," i.e., the substance and quiddity of things, 
although they treated this far too simply by defining things superficially. For in giving 
definitions they paid attention only to one thing; because they said that, if any given definition 
were to apply primarily to some thing, this would be the substance of that thing; just as if one 
were to suppose that the ratio "double" is the substance of the number two, because such a 
ratio is found first in the number two. And since being was found first in the one rather than 
in the many (for the many is composed of ones), they therefore said that being is the 
substance itself of the one. 

But this conclusion of theirs is not acceptable; for although the number two is double, the 
essence of twoness is not the same as that of the double in such a way that they are the same 
conceptually, as the definition and the thing defined. But even if their statements were true, it 
would follow that the many would be one. For some plurality can belong primarily to 
something one; for example, evenness and the ratio double belong first to the number two. 
Hence [according to them] it would follow that the even and the double are the same. And it 
would likewise follow that that to which the double belongs is the same as the number two, so 
long as the double is the substance of the number two. This, indeed, is also the conclusion 
which the Pythagoreans drew; for they attributed plurality and diversity to things as if they 
were one, just as they said that the properties of numbers are the same as the properties of 
natural beings. 


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150. Hence, Aristotle concludes that it is possible to learn this much from the early 
philosophers, who posited only one material principle, and from the later philosophers, who 
posited many principles. 


LESSON 10 

The Platonic Theory of Ideas 

ARISTOTLE'S TEXT Chapter 6: 987a 29-988a 17 

69. After the philosophies described came the system of Plato, which followed them in many 
respects, but also had other [theses] of its own in addition to the philosophy of the Italians. 
For Plato agreeing at the very beginning with the opinions of Cratylus (362) and Heraclitus 
that all sensible things are always in a state of flux, and that there is no scientific knowledge 
of them, also accepted this doctrine in later years. However, when Socrates, concerning 
himself with moral matters and neglecting nature as a whole, sought for the universal in these 
matters and fixed his thought on definition, Plato accepted him because of this kind of 
investigation, and assumed that this consideration refers to other entities and not to sensible 
ones. For [according to him] it is impossible that there should be a common definition of any 
one of these sensible things which are always changing. Such entities, then, he called Ideas or 
Forms (species); and he said that all sensible things exist because of them and in conformity 
with them; for there are many individuals of the same name because of participation in these 
Forms. With regard to participation, he [merely] changed the name; for while the 
Pythagoreans say that things exist by imitation of numbers, Plato says that they exist by 
participation, changing the name. Yet what this participation or imitation of Forms is they 
commonly neglected to investigate. 

70. Further, he says that besides sensible things and Ideas there are the objects of 
mathematics, which constitute an intermediate class. These differ from sensible things in 
being eternal and immobile; and from the Ideas in that there are many alike, whereas each 
Idea is itself only one. 

71. And since the Forms [or Ideas] are the causes of other things, he thought that the elements 
of these are the elements of all existing things. Hence, according to him, the great and small 
are principles as matter, and the one as substance [or form] ; for it is from these by 
participation in the one that the Ideas are numbers. 

72. Yet Plato said that the one is substance and that no other being is to be called one, just as 
the Pythagoreans did; and like them too he said that numbers are the causes of real substance. 


73. But to posit a dyad in place of the indeterminate one, and to produce the unlimited out of 
the great and small, is peculiar to him. Moreover, he says that numbers exist apart from 
sensible things, whereas they say that things themselves are numbers. Further, they do not 
maintain that the objects of mathematics are an intermediate class. 


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74. Therefore, his making the one and numbers to exist apart from things and not in things, as 
Pythagoreans did, and his introducing the separate Forms, were due to his investigation into 
the intelligible structures of things; for the earlier philosophers were ignorant of dialectic. 

75. But his making the dyad [or duality] to be a different nature was due to the fact that all 
numbers, with the exception of prime numbers, are naturally generated from the number two 
as a matrix. 

76. Yet what happens is the contrary of this. For this view is not a reasonable one; because the 
Platonists produce many things from matter but their form generates only once. 

77. And from one matter one measure seems to be produced, whereas he who induces the 
form, even though he is one, produces many measures. The male is also related to the female 
in a similar way; for the latter is impregnated by one act, but the male impregnates many 
females. And such are the changes in these principles. Concerning the causes under 
investigation, then, Plato defines them thus. 

78. From the foregoing account it is evident that Plato used only two causes: one being the the 
whatness of a thing, and the other, matter; for the Forms are the cause of the quiddity in other 
things, and the one is the cause of the quiddity in the Forms. What the underlying matter is of 
which the Forms are predicated in the case of sensible things, and the one in the case of the 
Forms, is also evident, namely, that it is this duality, the great and small. Moreover, he 
assigned the cause of good and evil to these two elements, one to each of them; which is 
rather a problem, as we say (48), that some of the first philosophers, such as Empedocles and 
Anaxagoras, [have attempted] to investigate. 

COMMENTARY 

Plato and form 

151. Having given the opinion of the ancient philosophers about the material and efficient 
cause, he gives a third opinion, that of Plato, who was the first to clearly introduce the formal 
cause. This is divided into two parts. First, he gives Plato's opinion. Second (171), from all of 
the foregoing remarks he makes a summary of the opinions which the other philosophers 
expressed about the four classes of causes ("We have examined"). 

In regard to the first he does two things. First, he gives Plato's opinion about the substances 
of things; and second (159), his opinion about the principles of things ("And since the 
Forms"). 

In regard to the first he does two things. First, he gives Plato's opinion insofar as he posited 
Ideas; and second (157), insofar as he posited intermediate substances, namely, the separate 
mathematical entities ("Further, he says"). 

He says, first, that after all the foregoing philosophers came the system of Plato, who 
immediately preceded Aristotle; for Aristotle is considered to have been his disciple. And 
even if Plato followed in many respects the natural philosophers who preceded him, such as 
Empedocles, Anaxagoras and the like, he nevertheless had certain other doctrines of his own 
in addition to those of the preceding philosophers, because of the philosophy of the Italians, 
or Pythagoreans. For insofar as he was devoted to the study of truth he sought out the 
philosophers of all lands in order to learn their teachings. Hence he came to Tarenturn in 


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Italy, and was instructed in the teachings of the Pythagoreans by Archytas of Tarenturn, a 
disciple of Pythagoras. 

152. Now Plato would seem to follow the natural philosophers who lived in Greece; and of 
this group some of the later members held that all sensible things are always in a state of flux, 
and that there can be no scientific knowledge of them (which was the position of Heraclitus 
and Cratylus). And since Plato became accustomed to positions of this kind from the very 
beginning, and agreed with these men in this position, which he acknowledged to be true in 
later years, he therefore said that scientific knowledge of particular sensible things must be 
abandoned. And Socrates (who was Plato's master and the disciple of Archelaus, a pupil of 
Anaxagoras), because of this position, which arose in his time, that there can be no science of 
sensible things, was unwilling to make any investigation into the nature of physical things, 
but only busied himself with moral matters. And in this field he first began to investigate 
what the universal is, and to insist upon the need for definition. 

153. Hence, Plato, being Socrates' pupil, "accepted Socrates," i.e., followed him, and adopted 
this method for the purpose of investigating natural beings. He did so believing that in their 
case the universal in them could successfully be grasped and a definition be assigned to it, 
with no definition being given for any sensible thing; because, since sensible things are 
always "changing," i.e., being changed, no common intelligible structure can be assigned to 
any of them. For every definition must conform to each thing defined and must always do so, 
and thus requires some kind of immutability. Hence universal entities of this kind, which are 
separate from sensible things and that to which definitions are assigned, he called the Ideas or 
Forms of sensible things. He called them Ideas, or exemplars, inasmuch as sensible things are 
made in likeness to them; and he called them Forms inasmuch as [sensible things] have 
substantial being by participating in them. Or he called them Ideas inasmuch as they are 
principles of being, and Forms inasmuch as they are principles of knowledge. Hence all 
sensible things have being because of them and in conformity with them. They have being 
because of the Ideas insofar as the Ideas are the causes of the being of sensible things, and "in 
conformity with them" insofar as they are the exemplars of sensible things. 

154. The truth of this is clear from the fact that "many individuals of the same name" are 
attributed to one Form alone, i.e., there are many individuals which have the same Form 
predicated of them, and predicated by participation. For the Form or Idea [of man] is the 
specific nature itself by which there exists man essentially. But an individual is man by 
participation inasmuch as the specific nature [man] is participated in by this designated 
matter. For that which is something in its entirety does not participate in it but is essentially 
identical with it, whereas that which is not something in its entirety but has this other thing 
joined to it, is said properly to participate in that thing. Thus, if heat were a self-subsistent 
heat, it would not be said to participate in heat, because it would contain nothing but heat. But 
since fire is something other than heat, it is said to participate in heat. 

155. In a similar way , since the separate Idea of man contains nothing but the specific nature 
itself, it is man essentially; and for this reason it was called by him man-in-itself. But since 
Socrates and Plato have in addition to their specific nature an individuating principle, which 
is designated matter, they are therefore said to participate in a Form, according to Plato. 

156. Now Plato took this term participation from Pythagoras, although [in doing so] he made 
a change in the term. For the Pythagoreans said that numbers are the causes of things, just as 
the Platonists said that the Ideas are, and claimed that sensible things of this kind exist as 
certain imitations of numbers. For inasmuch as numbers, which have no position of 


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themselves, received positions, they caused bodies. But because Plato held that the Ideas are 
unchangeable in order that there might be scientific knowledge of them, he did not agree that 
the term imitation could be used of the Ideas, but in place of it he used the term participation. 
However, it must be noted that, even though the Pythagoreans posited participation or 
imitation, they still did not investigate the way in which a common Form is participated in by 
individual sensible things or imitated by them. But the Platonists have treated this. 

157. Further, he says (70). 

Here he gives Plato's opinion about the mathematical substances. He says that Plato posited 
other substances — the objects of mathematics — in addition to the Forms and sensible things. 
Moreover, he said that beings of this kind were an intermediate class among the three kinds of 
substances; or that they were above sensible substances and below the Forms, and differed 
from both. The mathematical substances differed from sensible substances, because sensible 
substances are corruptible and changeable, whereas the mathematical substances are eternal 
and immobile. The Platonists got this idea from the way in which mathematical science 
conceives its objects; for mathematical science abstracts from motion. The mathematical 
substances also differed from the Forms, because the objects of mathematics are found to be 
numerically different and specifically the same, otherwise the demonstrations of mathematics 
would prove nothing. For unless two triangles belonged to the same class, geometry would 
attempt in vain to demonstrate that some triangles are alike; and the same thing is true of 
other figures. But this does not happen in the case of the Forms. For, since a Form is just the 
specific nature itself of a thing, each Form can only be unique. For even though the Form of 
man is one thing, and the Form of ass another thing, nevertheless the Form of man is unique, 
and so is the Form of ass; and the same thing is true of other things. 

158. Now to one who carefully examines Plato's arguments it is evident that Plato's opinion 
was false, because he believed that the mode of being which the thing known has in reality is 
the same as the one which it has in the act of being known. Therefore, since he found that our 
intellect understands abstractions in two ways: in one way as we understand universals 
abstracted from singulars, and in another way as we understand the objects of mathematics 
abstracted from sensible things, he claimed that for each abstraction of the intellect there is a 
corresponding abstraction in the essences of things. Hence he held that both the objects of 
mathematics and the Forms are separate. 

But this is not necessary. For even though the intellect understands things insofar as it 
becomes assimilated to them through the intelligible form by which it is put into act, it still is 
not necessary that a form should have the same mode of being in the intellect that it has in the 
thing known; for everything that exists in something else exists there according to the mode 
of the recipient. Therefore, considering the nature of the intellect, which is other than the 
nature of the thing known, the mode of understanding, by which the intellect understands, 
must be one kind of mode, and the mode of being, by which things exist, must be another. For 
although the object which the intellect understands must exist in reality, it does not exist there 
according to the same mode [which it has in the intellect]. Hence, even though the intellect 
understands mathematical entities without simultaneously understanding sensible substances, 
and understands universals without understanding particulars, it is not therefore necessary that 
the objects of mathematics should exist apart from sensible things, or that universals should 
exist apart from particulars. For we also see that sight perceives color apart from flavor, even 
though flavor and color are found together in sensible substances. 

159. And since the Forms (159). 


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Here he gives Plato's opinion concerning the principles of things; and in regard to this he 
does two things. First, he states the principles which Plato assigned to things; and second 
(169), the class of cause to which they are reduced ("From the foregoing"). 

In regard to the first he does two things. First, he tells us what kind of principles Plato had 
assigned to things. Second (160), he shows in what respect Plato agreed with the 
Pythagoreans, and in what respect he differed from them ("Yet Plato"). 

He says, first, that, since the Forms are the causes of all other beings according to Plato, the 
Platonists therefore thought that the elements of the Forms are the elements of all beings. 
Hence, they assigned as the material principle of things the great and small, and said that "the 
substance of things," i.e., their form, is the one. They did this because they held these to be 
the principles of the Forms. For they said that just as the Forms are the formal principles of 
sensible things, in a similar way the one is the formal principle of the Forms. Therefore, just 
as sensible things are constituted of universal principles by participation in the Forms, in a 
similar way the Forms, which he said are numbers, are constituted "of these," i.e., of the great 
and small. For the unit constitutes different species of numbers by addition and subtraction, in 
which the notion of the great and small consists. Hence, since the one was thought to be the 
substance of being (because he did not distinguish between the one which is the principle of 
number, and the one which is convertible with being), it seemed to him that a plurality of 
different Forms might be produced from the one, which is their common substance, in the 
same way that a plurality of different species of numbers is produced from the unit. 

160. Yet Plato (72). 

Here he compares the position of Plato with that of Pythagoras. First, he shows in what 
respect they agreed; and second (160), in what respect they differed ("But to posit"). 

Now they agreed in two positions; (1) and the first is that the one is the substance of things. 
For the Platonists, like the Pythagoreans, said that what I call the one is not predicated' of 
some other being as an accident is of a subject, but signifies a thing's substance. They said 
this, as we have pointed out (159), because they did not distinguish between the one which is 
convertible with being and the one which is the principle of number. 

161. (2) The second position follows from the first; for the Platonists, like the Pythagoreans, 
said that numbers are the causes of the substance of all beings; and they held this because [in 
their opinion] number is just a collection of units. Hence if the one is substance, number must 
also be such. 

162. But to posit (73). 

Here he shows in what respect they differed; and in regard to this he does two things. First, he 
states how they differed. Second (164), he gives the reason for this difference ("Therefore, his 
making"). 

Now this difference involves two things. First, the Pythagoreans, as has already been stated, 
posited two principles of which things are constituted, namely, the limited and the unlimited, 
of which one, i.e., the unlimited, has the character of matter. But in place of this one 
principle — the unlimited — which the Pythagoreans posited, Plato created a dyad, holding that 
the great and small have the character of matter. Hence the unlimited, which Pythagoras 
claimed to be one principle, Plato claimed to consist of the great and small. This is his own 


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opinion in contrast with that of Pythagoras. 

163. The second difference is that Plato held that numbers are separate from sensible things, 
and this in two ways. For he said that the Forms themselves are numbers, as was pointed out 
above (159); and he also held, as was stated above (157), that the objects of mathematics are 
an intermediate class between the Forms and sensible things, and that they are numbers by 
their very essence. But the Pythagoreans said that sensible things themselves are numbers, 
and did not make the objects of mathematics an intermediate class between the Forms and 
sensible things; nor again did they hold that the Forms are separate from things. 

164. Therefore, his making (74). 

Here he gives the reason for the difference. First, he gives the reason for the second 
difference; and then (165), the reason for the first difference. 

He says, then, that the Platonists adopted the position that both the one and numbers exist 
apart from sensible things and not in sensible things, as the Pythagoreans claimed; and they 
also introduced separate Forms because of the investigation "which was made into the 
intelligible structures of things," i.e., because of their investigation of the definitions of 
things, which they thought could not be attributed to sensible substances, as has been stated 
(150). This is the reason they were compelled to hold that there are certain things to which 
definitions are assigned. But the Pythagoreans, who came before Plato, were ignorant of 
dialectic, whose office it is to investigate definitions and universals of this kind, the study of 
which led to the introduction of the Ideas. 

165. But his making (75). 

Here he gives the reason for the other difference, that is, the one concerning matter. First, he 
gives the reason for such a difference. Second (166), he shows that Plato was not reasonably 
motivated. 

He accordingly says that the Platonists made the dyad [or duality] to be a number of a 
different nature than the Forms, because all numbers with the exception of prime numbers are 
produced from it. They called prime numbers those which are not measured by any other 
number, such as three, five, seven, eleven, and so on; for these are produced immediately 
from unity alone. But numbers which are measured by some other number are not called 
prime numbers but composite ones, for example, the number four, which is measured by the 
number two; and in general every even number is measured by the number two. Hence even 
numbers are attributed to matter, since unlimitedness, which belongs to matter, is attributed to 
them, as has been stated above (125). This is why he posited the dyad, from which as "a 
matrix," or exemplar, all other even numbers are produced. 

166. Yet what happens (76). 

Here he proves that Plato made unreasonable assumptions; and in regard to this he does two 
things. For, first, he proves this by an argument from nature. Second (167), he gives the 
argument based on the nature of things, which led Plato to adopt this position ("And from one 
matter"). 

He says that, although Plato posited a dyad on the part of matter, still what happens is the 
contrary of this, as the opinions of all the other natural philosophers testify; for they claimed 


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that contrariety pertains to form and unity to matter, as is clear in Book I of the Physics. For 
they held that the material principle of things is air or water or something of this kind, from 
which the diversity of things is produced by rarefaction and condensation, which they 
regarded as formal principles; for Plato's position is not a reasonable one. Now the natural 
philosophers adopted this position because they saw that many things are generated from 
matter as a result of a succession of forms in matter. For that matter which now supports one 
form may afterwards support many forms as a result of one form being corrupted and another 
being generated. But one specifying principle or form "generates only once," i.e., constitutes 
the thing which is generated. For when something is generated it receives a form, and the 
same form numerically cannot become the form of another thing that is generated, but ceases 
to be when that which was generated undergoes corruption. In this argument it is clearly 
apparent that one matter is related to many forms, and not the reverse, i.e., one form to many 
matters. Thus it seems more reasonable to hold that unity pertains to matter but duality or 
contrariety to form, as the philosophers of nature claimed. This is the opposite of what Plato 
held. 

167. And from one matter (77). 

Here he gives an opposite argument taken from sensible things according to the opinion of 
Plato. For Plato saw that each thing is received in something else according to the measure of 
the recipient. Hence receptions seem to differ according as the capacities of recipients differ. 
But one matter is one capacity for reception. And Plato also saw that the agent who induces 
the form, although he is one, causes many things to have this form; and this comes about 
because of diversity on the part of matter. An example of this is evident in the case of male 
and female; for a male is related to a female as an agent and one who impresses a form on 
matter. But a female is impregnated by one act of a male, whereas one male can impregnate 
many females. This is why he held that unity pertains to form and duality to matter. 

168. Now we must note that this difference between Plato and the philosophers of nature is a 
result of the fact that they considered things from different points of view. For the 
philosophers of nature considered sensible things only insofar as they are subject to change, 
in which one subject successively acquires contrary qualities. 

Hence they attributed unity to matter and contrariety to form. But Plato, because of his 
investigation of universals, went on to give the principles of sensible things. Therefore, since 
the cause of the diversity of the many singular things which come under one universal is the 
division of matter, he held that diversity pertains to matter and unity to form. "And such are 
the changes of those principles" which Plato posited, i.e., participations, or, as I may say, 
influences in the things generated. For Pythagoras understands the word change in this way. 
Or Aristotle says "changes" inasmuch as Plato changed the opinion which the first 
philosophers of nature had about principles, as is evident from the foregoing. Hence it is 
evident from the foregoing that Plato dealt thus with the causes which we are investigating. 

169. From the foregoing (78). 

Here he shows to what class of cause the principles given by Plato are referred. He says that it 
is evident from the foregoing that Plato used only two kinds of causes. For he used as "one" 
cause of a thing the cause of its "whatness," i.e., its quiddity, or its formal cause, which 
determines its quiddity; and he also used matter itself. This is also evident from the fact that 
the Forms which he posited "are the causes of other things," i.e., the causes of the whatness of 
sensible things, namely, their formal causes, whereas the formal cause of the Forms 


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themselves is what I call the one, which seems to be the substance of which the Forms are 
composed. And just as he holds that the one is the formal cause of the Forms, in a similar 
fashion he holds that the great and small are their material cause, as was stated above (159). 
And these causes — the formal and the material cause — are referred not only to the Forms but 
also to sensible substances, because [there is some subject of which] the one is predicated in 
the case of the Forms. That is to say, that which is related to sensible substances in the same 
way as the one is to the Forms is itself a Form, because that duality which relates to sensible 
things as their matter is the great and small. 

170. Furthermore, Plato indicated the cause of good and evil in the world, and he did this with 
reference to each of the elements which he posited. For he made Form the cause of good and 
matter the cause of evil. 

However, some of the first philosophers attempted to investigate the cause of good and evil, 
namely, Anaxagoras and Empedocles, who established certain causes in the world with this 
special end in view that by means of these causes they might be able to give the principles of 
good and evil. And in touching upon these causes of good and evil they came very close to 
positing the final cause, although they did not posit this cause directly but only indirectly, as 
is stated below (177). 


LESSON 11 

A Summary of the Early Opinions about the Causes 
ARISTOTLE'S TEXT Chapter 7: 988a 18-988b 21 

79. We have examined, then, in a brief and summary way those philosophers who' have 
spoken about the principles of things and about the truth, and the way in which they did this. 
Yet we have learned from them this much: that none of those who have discussed principle 
and cause have said anything beyond the points established by us in the Physics. 

80. Yet all have approached these causes obscurely. 

81. For some speak of the [first] principle as matter, whether they suppose it to be one or 
many, and whether they assume it to be a body or something incorporeal, as Plato speaks of 
the great and small; the Italians of the unlimited; Empedocles of fire, earth, water and air; and 
Anaxagoras of an infinite number of like parts. All these have touched on this kind of cause, 
and so also have those who make the first principle air or fire or water or something denser 
than fire or rarer than air. For they have said that some such body is the primary element. 
These thinkers, then, have touched only on this cause. 

82. But others [have introduced] the source of motion, for example, those who make 
friendship and strife, or intellect, or love, or something besides these, a principle of things. 

83. But the quiddity or substance no one has presented clearly. Those who express it best are 
those wbo posit the Ideas and the intelligible natures inherent in the Ideas. For they do not 
think of the Ideas and the things inherent in them as the matter of sensible things; nor do they 


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think of them as the source from which motion originates, for they say that these things are 
the causes rather of immobility and of that which is at rest. But [according to them] the Forms 
are responsible for the quiddity of all other things, and the one for the quiddity of the Forms. 

84. That for the sake of which there are actions and changes and motions they affirm in some 
way to be a cause, but not in the way we are determining causes, or in the way in which it is 
truly a cause. For while those who speak of intellect or love posit these causes as good, they 
do not say that anything exists or comes to be because of them, but claim that the motion of 
things stems from them. In like manner those who say that the one or being is such a reality, 
say that it is the cause of substance, but not that things either are or come to be for the sake of 
this. Hence, it happens to them that in a way they both say and do not say that the good is a 
cause; for they do not speak of it in its principal aspect but in a secondary one. 

85. Therefore all these philosophers, being unable to touch on any other cause, seem to bear 
witness to the fact that we have dealt correctly with the causes, both as to their number and 
their kinds. Moreover, it is evident that all principles must be sought in this way or in some 
similar one. As to the way in which each of these philosophers has spoken, and how they 
have raised possible problems about the principles of things, let us discuss these points next. 

COMMENTARY 

171. Here he makes a summary of everything that the early philosophers have said about 
causes* and in regard to this he does three' things. First (79:C 171), he shows that the early 
philosophers were unable to add artother kind of cause to the four classes of causes given 
above (34:C 70). Second (80:C 172), he indicates the way in which they touched upon these 
causes ("Yet all"). Third (85 :C 180) he draws the conclusion at which he chiefly aims 
("Therefore all these"). 

He says, first (79), that in giving this brief and summary account he has stated who the 
philosophers are, and how they have spoken of the principles of things and of what is true of 
the substance itself of things. And from their statements this much can be learned: that none 
of those who have spoken about causes and principles were able to mention any causes other 
than those distinguished in Book II of the Physics. 

172. Yet all (80). 

Here he gives the way in which they dealt with each of the causes. He does this, first (80), in 
a general way: and, second (81:C 172), in a special Way ("For some speak"). 

Accordingly be says, first, that they not only have not added anything, but in the way in 
which they approached these causes they proceeded obscurely and not clearly. For they have 
not stated to what class of cause the principles posited by them would belong; but they gave 
as principles things that can be adapted to some class of cause. 

173. For some speak (81). 

Here he shows in a special way how they touched on each of these causes. He shows, first 
(81), how they touched on the material cause; second (82:C 174), On the efficient cause ("But 
others"); third (83:C 175), on the formal cause ("But the quiddity"); and fourth (84:C 177), on 
the final cause ("That for the sake of which"). 


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He says, first (81), then, that those philosophers, i.e., the early ones, all agree insofar as they 
assign some material cause to things. Yet they differ in two respects. First, they differ in that 
some, such as Thales, Diogenes and the like, held that the material principle is one, whereas 
others, such as Empedocles, claimed that it is many; and second, they differ in that some, 
such as the first group above, held that the material principle of things is a body, whereas 
others, such as Plato, who posited a dyad, claimed that it is something incorporeal. For Plato 
posited the great and small, which the Platonists do not speak of as a body. The Italians, or 
Pythagoreans, posited the unlimited ; but neither is this a body. Empedocles, on the other 
hand, posited the four elements, which are bodies; and Anaxagoras also posited "an infinite 
number of like parts," i.e.) [he claimed] that the principles of things are an infinite number of 
like parts. All of these thinkers have touched on "this kind of cause," i.e., the material cause, 
and so also have those who said that the principle of things is air or water or fire or something 
midway between these elements, i.e., what is denser than fire and rarer than air. For all 
philosophers such as those just mentioned have claimed that some kind of body is the first 
element of things. Thus Aristotle's statement is evident, namely, that in the light of the 
foregoing remarks these philosophers have posited only the material cause. 

174. But others (82). 

Here he gives their opinions about the efficient cause. He says that some of the foregoing 
philosophers have posited, in addition to the material cause, a cause from which motion 
begins, for example, those who made love or hate or intellect a cause of things, or those who 
introduced some other active principle distinct from these, as Parmenides, who made fire an 
efficient cause. 

175. But the quiddity (83) 

Here he gives their opinions about the formal cause. He says that the cause through which a 
thing's substance is known, i.e., the formal cause, no one attributed to things with any clarity. 
And if the ancient philosophers touched on something that might pertain to the formal cause, 
as Empedocles did when he claimed that bone and flesh contain some proportion [of the 
elements] , by which they are things of this kind, nevertheless they did not treat what belongs 
to the formal cause after the manner of a cause. 

176. But among the other philosophers, those who posited the Forms and those intelligible 
aspects which belong to the Forms, such as unity, number and the like, came closest to 
positing the formal cause. For the Forms and everything that belongs to the Forms in the 
aforesaid way, such as unity and number, are not acknowledged or assumed by them to be the 
matter of sensible things, since they place matter rather on the side of sensible things; nor do 
they claim that the Forms are the causes from which motion originates in the world, but rather 
that they are the cause of immobility in things. For they said that whatever is found to be 
necessary in sensible things is caused by the Forms, and that these, i.e., the Forms, are 
immobile. For they claimed that the Forms, because immobile, are uniform in being, as has 
been said (69:C 156), so that definitions can be given of them and demonstrations made about 
them. But according to the opinion of these men the Forms are responsible for the quiddity of 
pparticular things after the manner of a formal cause, and the one is responsible for the 
quiddity of the Forms. 

All the foregoing weak on FINAL cause 


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177. That for the sake of which (84). Here he gives the opinions of certain thinkers about 
the final cause. He says that in one sense the philosophers say that the goal for the sake of 
which motions, changes and activities occur is a cause, and in another sense they do not. And 
they neither speak of it in the same way, nor in the way in which it is a true cause. For those 
who affirm that intellect or love is a cause, posit these causes as good. For they said that 
things of this kind are the causes of things being well disposed, since the cause of good can 
only be good. Hence it follows that they could make intellect and love to be causes, just as the 
good is a cause. But good can be understood in two ways: (1) in one way as a final cause, in 
the sense that something comes to be for the sake of some good; and (2) in another way as an 
efficient cause, as we say that the good man does good. 

Now these philosophers did not say that the foregoing causes are good in the sense that they 
are the reason for the existence or coming to be of some beings, which pertains to the 
intelligibility of the final cause, but in the sense that there proceeds from these 
causes — intellect and will — a kind of motion toward the being and coming-to-be of things; 
and this pertains to the intelligibility of the efficient cause. 

178. In a similar way the Pythagoreans and Platonists, who said that the substance of things is 
the one itself or being, also attributed goodness to the one or being. Thus they said that such a 
reality, i.e., the good, is the cause of the substance of sensible things, either in the manner of a 
formal cause, as the Platonists maintained, or in the manner of a material cause, as the 
Pythagoreans claimed. 

However, they did not say that the being and coming-to-be of things exists for the sake of 
this, i.e., the one or being; and this is something that pertains to the intelligibility of the final 
cause. 

Hence, just as the philosophers of nature claimed that the good is a cause in the manner of an 
(+) efficient cause and not in that of a (~) formal cause, in a similar way the Platonists 
claimed that the good is a cause in the manner of a (+) formal cause, and not in that of a (~) 
final cause. The Pythagoreans, on the other hand, considered it to be a cause in the manner of 
a (+) material cause. 

179. It is evident, then, that in one sense they happened to speak of the good as a cause and in 
another not. For they did not speak of it as a cause in its principal aspect but in a secondary 
one; because according to its proper intelligible structure the good is a cause in the manner of 
a final cause. This is clear from the fact that the good is what all desire. Now that to which an 
appetite tends is a goal. Therefore according to its proper intelligible structure the good is a 
cause in the manner of a goal. 

Hence those who make the good a cause in its principal aspect claim that it is a final cause. 
But those who attribute a different mode of causality to the good claim that the good is a 
cause but only in a secondary way; because they do not hold that it is such by reason of being 
good, but by reason of that to which good happens to belong by reason of its being active or 
perfective. 

Hence it is clear that those philosophers posited a final cause only incidentally, because they 
posited as a cause something that is fitting to be an end, namely, the good. However, they did 
not claim that it is a cause in the manner of a final cause, as has been stated. 

Conclusion 


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180. Therefore all these (85). 

Here he draws the conclusion at which he chiefly aims: that the things established about the 
causes, both as to their number and their kinds, are correct. For the foregoing philosophers 
seem to bear witness to this in being unable to add another class of cause to those discussed 
above. This is one of the useful pieces of information resulting from the account of the 
foregoing views. 

Another is that evidently the principles of things must be investigated in this science, either 
all those which the ancient philosophers posited, and which have been established above, or 
some of them. For this science considers chiefly the formal and final cause, and also in a 
sense the efficient cause. 

Now it is not only necessary that the above views be discussed, but after this examination it is 
also necessary to describe the way in which each of these men has spoken (both in what sense 
their statements are acceptable and in what sense not), and how the statements which have 
been made about the principles of things contain a problem. 


LESSON 12 

Criticism of the Views about the Number of Material Principles 
ARISTOTLE'S TEXT Chapter 8: 988b 22-98% 24 

86. Therefore all those who hold that the whole is one and say that there is a certain single 
nature as matter, and that this is corporeal and has measure, are clearly at fault in many ways. 
For they give only the elements of bodies and not those of incorporeal things, as if 
incorporeal things did not exist. 

87. And in attempting to state the cause of generation and corruption, and in treating all things 
according to the method of natural philosophy, they do away with the cause of motion. 

88. Furthermore, they did not claim that the substance or whatness of a thing is a cause of 
anything. 

89. And they were wrong in holding that any of the simple bodies except earth is a principle, 
without considering how they are generated from each other. 

90. 1 mean fire, earth, water and air; for some of these are generated from each other by 
combination and others by separation. Now it makes the greatest difference as to which of 
these is prior and which subsequent. 

91. For in one way it would seem that the most basic element of all is that from which a thing 
first comes to be by combination. But such an element will be one which has the smallest 
parts and is the subtlest of bodies. Hence all those who posit fire as the first principle make 
statements that conform most closely to this theory. But each of the other thinkers admits that 
the primary element of bodies is something of this kind. 


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92. For none of the later thinkers, and none of those who spoke about the one, wanted earth to 
be an element, evidently because of the size of its particles. But each of the other three 
elements finds some supporter, for some say that this primary element is fire, others water, 
and others air. But why do they not say that it is earth, as in a sense most men do? For they 
say that everything is earth. And Hesiod says that earth is the first of bodies to be generated; 
for this happens to be the ancient and common view. Therefore, according to this theory, if 
anyone says that any of these bodies with the exception of fire is the primary element of 
things, or if anyone holds that it is something denser than air but rarer than water, he will not 
speak the truth. 

93. However, if that which is later in generation is prior in nature, and if that which is 
condensed and compounded is later in generation, then the reverse will be true — water will be 
prior to air, and earth to water. Let these points suffice, then, regarding those who posit one 
cause such as we have described. 

94. The same consequence will also be true if anyone posits many elements, as Empedocles 
says that the four [elemental] bodies are the matter of things. For these same consequences 
must befall this man, as well as some which are peculiar to himself. For we see things being 
generated from each other in such a way that the same body does not always remain fire or 
earth. But we have spoken of these matters in our physical treatises. 

95. And concerning the cause of things in motion, whether one or more than one must be 
posited, it must not be thought that what has been said is either entirely correct or reasonable. 

96. And in general those who speak thus must do away with alteration, because the cold will 
not come from the hot, nor the hot from the cold. For what is it that undergoes these 
contraries and what is the one nature which becomes fire and water? Such a thing 
Empedocles does not admit. 

97. But if anyone were to maintain that Anaxagoras speaks of two elements, they would 
acknowledge something fully in accord with a theory which he himself has not stated 
articulately, although he would have been forced to follow those who express this view. For 
to say, as he did, that in the beginning all things are mixed together is absurd, both because it 
would be necessary to understand that things previously existed in an unmixed state, and 
because it is not fitting that anything should be mixed with just anything; and also because 
properties and accidents could be separated from substances (for there is both mixture and 
separation of the same things). Yet, if anyone were to follow him up and articulate what he 
means, his statement would perhaps appear more astonishing. For when nothing was distinct 
from anything else, evidently nothing would be truly predicated of that substance. I mean that 
it would neither be white nor black nor tawny, nor have any color, but would necessarily be 
colorless; for otherwise it would have one of these colors. And, similarly, it would be without 
humors. And for the same reason it would have no other similar attribute. For it could not 
have any quality or quantity or whatness, because, if it had, some of the attributes described 
as formal principles would inhere in it. But this is obviously impossible, since all things are 
mixed together; for they would already be distinct from each other. But he said that all things 
are mixed together except intellect, and that this alone is unmixed and pure.' Now from these 
statements it follows for him that there are two principles, one being the intellect itself (for 
this is unmixed in an absolute sense), and the other being the kind of thing we suppose the 
indeterminate to be before it is limited and participates in a form. Hence, what he says is 
neither correct nor clear, although he intends something similar to what later thinkers said and 
what is now more apparent. But these thinkers are concerned only with theories proper to 


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generation, corruption and motion; for usually it is only of this kind of substance that these 
men seek the principles and causes. 

COMMENTARY 

181. Having stated the opinions which the philosophers held about the principles of things, 
Aristotle begins here to criticize them; and this is divided into two parts. First, he criticizes 
each opinion. Second (272), he summarizes his discussion and links it up with what follows 
("From the foregoing"). 

The first is divided into two parts. First, he criticizes the opinions of those who have treated 
things according to the method of natural philosophy. Second (201), he criticizes the opinions 
of those who have not treated things according to the method of natural philosophy, i.e., 
Pythagoras and Plato, because they posited higher principles than the natural philosophers did 
("But all those"). 

In regard to the first part he does two things. First, he criticizes the opinions of those who 
posited one material cause; and second (190), the opinions of those who posited many ("The 
same consequence"). 

In regard to the first he does two things. First, he criticizes the foregoing opinions in a general 
way; and second (183), in a special way ("And they were wrong"). 

He criticizes these opinions in a general way by means of three arguments. The first (86) is 
this: in the world there are not only bodies but also certain incorporeal things, as is clear from 
The Soul. But these men posited only corporeal principles, which is clear from the fact that 
they maintained that "the whole is one," i.e., that the universe is one thing substantially, and 
that there is a single nature as matter, and that this is corporeal and has "measure," i.e., 
dimension. But a body cannot be the cause of an incorporeal thing. Therefore it is evident that 
they were at fault in this respect that they treated the principles of things inadequately. And 
they were at fault not only in this respect but in many others, as is clear from the following 
arguments. 

182. And in attempting (87). 

Here he gives the second argument, which runs thus: whoever feels obliged to establish the 
truth about motion must posit a cause of motion. But these philosophers felt obliged to treat 
motion, which is clear for two reasons: first, because they tried to state the causes of 
generation and corruption in the world, which do not occur without motion; and second, 
because they wanted to treat things according to the method of natural philosophy. But since a 
treatment of things according to this method involves motion (because nature is a principle of 
motion and rest, as is clear in Book II of the Physics), they should therefore have dealt with 
that cause which is the source of motion. And since they did away with the cause of motion 
by saying nothing about it, obviously they were also at fault in this respect. 

183. Furthermore, they did not (88). 

Here he gives the third argument: every natural being has "a substance," i.e., aform of the 
part, "and whatness," i.e., quiddity, which is the form of the whole.3 He says form inasmuch 
as it is a principle of subsistence, and whatness inasmuch as it is a principle of knowing, 
because what a thing is is known by means of this. But the foregoing philosophers did not 


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claim that form is a cause of anything. They treated things inadequately, then, and were also 
at fault in neglecting the formal cause. 

184. For none of the later (92). 

Here he criticizes their opinions in a special way; and he does this with respect to two things. 
First, he criticizes them for maintaining that all the elements with the exception of fire are the 
principles of things. Second (187), he criticizes them for omitting earth ("However, if). 

First (92), he takes up once more the position of those who claimed that each of the simple 
bodies except earth is the [primary] element of things. The reason which he gives for this 
position is that these men saw that the simple bodies are generated from each other in such a 
way that some come from others by combination or compacting, as grosser things come from 
more refined ones. 

185. He also explains how to proceed against their opinions from their own arguments. For 
they claimed that one of these elements is the principle of things by arguing that other things 
are generated from it either by combination or by separation. Now it makes the greatest 
difference as to which of these two ways is prior and which subsequent, for on this depends 
the priority or posteriority of that from which something is generated. For, on the one hand, 
that seems to be prior from which something is produced by combination; and he gives this 
argument first. Yet, on the other hand, that seems to be prior from which something is 
produced by rarefaction; and he bases his second argument on this. 

186. For the fact that the primary element is that from which something is produced by 
combination supports the opinion which is now held that the most basic element is that from 
which other things are produced by combination. This in fact is evident both from reason and 
from the things that they held. It is evident from reason, because that from which other things 
are produced by combination is the most refined type of body, and the one having the 
smallest parts; and this seems to be the simpler body. Hence, if the simple is prior to the 
composite, this body seems to be first. It is also evident from the things that they held, 
because all those who posited fire as the principle of things asserted that it is the first 
principle. Similarly, others have been seen to follow this argument, for they thought that the 
primary element of bodies is the one having the finest parts. This is evident from the fact that 
none of the later philosophers followed the theological poets, who said that earth is the 
primary element of things. Evidently they refused to do this "because of the size of its parts," 
i.e., because of the coarseness of its parts. However, it is a fact that each of the other three 
elements finds some philosopher who judges it to be the principle of things. But their refusal 
to make earth a principle is not to be explained by a refusal to reject a common opinion; for 
many men thought that earth is the substance of things. Hesiod, who was one of the 
theological poets, also said that earth is the first of all bodies to come into 

being. Thus the opinion that earth is the principle of things is evidently an ancient one, 
because it was maintained by the theological poets, who preceded the philosophers of nature. 
It was also the common opinion, because many men accepted it. It follows, then, that the later 
philosophers 

avoided the position that earth is a principle only because of the coarseness of its parts. But it 
is certain that earth has coarser parts than water, and water than air, and air than fire; and if 
there is any intermediate element, it is evident that it is grosser than fire. Hence by following 
this argument it is clear that none of them spoke correctly, except him who held that fire is the 


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first principle. For as soon as some element is held to be a principle by reason of its 
minuteness, the most minute element must be held to be the first principle of things. 

187. However, if that which (93). 

Here he gives another argument, and according to it the opposite seems to be true, namely, 
that earth is the most basic element of things. For it is evident that whatever is subsequent in 
generation is prior in nature, because nature tends to the goal of generation as the first thing in 
its intention. But the denser and more composite something is, the later it appears in the 
process of generation; for the process of generation proceeds from simple things to composite 
ones, Just as mixed bodies come from the elements, and the humors and members [of a living 
body] from mixed bodies. Hence, whatever is more composite and condensed is prior in 
nature. In this way a conclusion is reached which is the opposite of that following from the 
first argument; i.e., water is now prior to air and earth to water as the first principle of things. 

188. It should be noted, however, that it is a different thing to look for what is prior in one 
and the same entity and for what is prior without qualification. For if one seeks what is prior 
without qualification, the perfect must be prior to the imperfect, just as actuality is prior to 
potentiality; because a thing is brought from a state of imperfection to one of perfection, or 
from potentiality to actuality, only by something completely actual. Therefore, if we speak of 
what is first in the whole universe, it must be the most perfect thing. But in the case of one 
particular thing which goes from potentiality to. complete actuality, potentiality is prior to 
actuality in time, although it is subsequent in nature. It is also clear that the first of all things 
must be one that is simplest; for the composite depends on the simple, and not the reverse. It 
was necessary, then, that the ancient philosophers should attribute both of these properties 
(the greatest perfection along with the greatest simplicity) to the first principle of the whole 
universe. However, these two properties cannot be attributed simultaneously to any corporeal 
principle, for in bodies subject to generation and corruption the simplest entities are 
imperfect. They were Compelled, then, as by contrary arguments, to posit different principles. 
Yet they preferred the argument of simplicity, because they considered things only insofar as 
something passes from potentiality to actuality, and in this order it is not necessary that 
anything which is a principle should be more perfect. But this kind of opposition can be 
resolved only by maintaining that the first principle of things is incorporeal, because this 
principle will be the simplest one, as Aristotle will prove below (2548). 

189. Last of all he concludes that for the purpose of the present discussion enough has been 
said about the positions of those who affirm one material cause. 

190. The same consequence (94). 

Here he gives the arguments against those who posited many material causes. First, he argues 
against Empedocles; and second (194), against Anaxagoras ("But if anyone"). 

First (94), he says that the same consequence faces Empedocles, who held that the four 
[elemental] bodies are the matter of things, because he experienced the same difficulty with 
regard to the above contrariety. For according to the argument of simplicity fire would seem 
to be the most basic principle of bodies; and according to the other argument earth would 
seem to be such, as has been stated (187). And while Empedocles faced some of the same 
absurd conclusions as the preceding philosophers (i.e., he did not posit either a formal cause 
or 


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the aforesaid contrariety of simplicity and perfection in corporeal things), there is no 
argument against him for doing away with the cause of motion. But he did face certain other 
absurd conclusions besides those that confronted the philosophers who posited one material 
cause. 

191. This is shown by three arguments, of which the first is as follows. 

First principles are not generated from each other, because a principle must always remain in 
existence, as is pointed out in Book I of the Physics. But we perceive that the four elements 
are 

generated from each other, and for this reason their generation is dealt with in natural 
philosophy. Hence his position that the four elements are the first principles of things is 
untenable. 

192. And concerning the cause (95). 

Here he gives the second absurdity, which has to do with the cause of motion. For to posit 
many and contrary causes of motion is not at all correct or reasonable; because if the causes 
of motion are understood to be proximate ones, they must be contraries, since their effects 
seem to be contraries. But if the first cause is understood, then it must be unique, as is 
apparent in Book XII (2492) of this work, and in Book VIII of the Physics. Therefore, since 
he intends to posit the first causes of motion, his position that they are contraries is untenable. 

193. And in general (96). 

Here he gives the third argument which leads to an absurdity: in every process of alteration it 
must be the same subject which undergoes contraries. This is true because one contrary does 
not come from another in such a way that one is converted into the other; for example, the 
cold does not come from the hot in such a way that heat itself becomes cold or the reverse, 
although the cold does come from the hot when the underlying subject is one only inasmuch 
as the single subject which is now the subject of heat is afterwards the subject of cold. But 
Empedocles did not hold that contraries have one subject. In fact he held that they are found 
in different subjects, as heat in fire and cold in water. Nor again did he hold that there is one 
nature underlying these two. Therefore he could not posit alteration in any way. Yet it is 
absurd that alteration should be done away with altogether. 

194. But if anyone (97). 

Here he deals with Anaxagoras' opinion; and in regard to this he does two things. First, he 
shows in general in what respect Anaxagoras' opinion should be accepted as true, and in what 
respect not. Second (97), he explains each of these in particular ("For to say"). 

He says, first, that if anyone wishes to maintain that Anaxagoras' opinion is true insofar as he 
posited two principles, i.e., matter and efficient cause, let him understand this according to the 
reasoning which Anaxagoras himself seems to have followed, as if compelled by some need 
for truth, inasmuch as he would have followed those who expressed this theory. But "he 
himself has not stated it articulately"; i.e., he has not expressed it distinctly. Therefore, with 
reference to what he has not expressly stated his opinion is true; but with reference to what he 
has expressly stated his opinion is false. 


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195. This is made clear in particular as follows. If his opinion is taken in its entirety according 
to a superficial understanding of his statements, a greater absurdity will appear for four 
reasons. First, his opinion that all things were mixed together at the beginning of the world is 
absurd; for in Aristotle's opinion the distinction between the parts of the world is thought to 
be eternal. The second reason is this: what is unmixed is related to what is mixed as the 
simple to the composite. But simple bodies are prior to composite ones, and not the reverse. 
Therefore what is unmixed must be prior to what is mixed. This is the opposite of what 
Anaxagoras said. The third reason is this: in the case of bodies not anything at all is naturally 
disposed to be mixed with anything else, but only those things are naturally disposed to be 
mixed which are naturally inclined to pass over into each other by some kind of alteration; for 
a mixture is a union of the altered things which are capable of being mixed. But Anaxagoras 
held that anything is mixed with just anything. The fourth reason is this: there is both mixture 
and separation of the same things; for only those things are said to be mixed which are 
naturally disposed to exist apart. But properties and accidents are mixed with substances, as 
Anaxagoras said. Therefore it follows that properties and accidents can exist apart from 
substances. This is evidently false. These absurdities appear then, if Anaxagoras' opinion is 
considered in a superficial way. 

196. Yet if anyone were to follow him up "and articulate," i.e., investigate clearly and 
distinctly, the things which Anaxagoras "means," i.e., what he intended, although he did not 
know how to express this, his statement would appear to be more astonishing and subtler than 
those of the preceding philosophers. This will be so for two reasons. First, he came closer to a 
true understanding of matter. This is clear from the fact that in that mixture of things, when 
nothing was distinguished from anything else but all things were mixed together, nothing 
could be truly predicated of that substance which is so mixed, which he held to be the matter 
of things. This is clear in the case of colors; for no special color could be predicated of it so 
that it might be said to be white or black or have some other color; because, according to this, 
that color would necessarily be unmixed with other things. Nor, similarly, could color in 
general be predicated of it so that it might be said to be colored; because everything of which 
a generic term is predicated must also have a specific term predicated of it, whether the 
predication be univocal or denominative. Hence, if that substance were colored, it would 
necessarily have some special color. But this is opposed to the foregoing statement. And the 
argument is similar with respect to "humors," i.e., savors, and to all other things of this kind. 
Hence the primary genera themselves could not be predicated of it in such a way that it would 
have quality or quantity or some attribute of this kind. For if these genera were predicated of 
it, some particular species would necessarily belong to it. But this is impossible, if all things 
are held to be mixed together. For this species which would be predicated of that substance 
would already be distinguished from the others. And this is the true nature of matter, namely, 
that it does not have any form actually but is in potentiality to all forms. For the mixed body 
itself does not have actually any of the things which combine in its mixture, but has them only 
potentially. And it is because of this likeness between prime matter and what is mixed that he 
seems to have posited the above mixture; although there is some difference between the 
potentiality of matter and that of a mixture. For even though the elements which constitute a 
mixture are present in the mixture potentially, they are still not present in a state of pure 
passive potency; for they remain virtually in the mixture. This can be shown from the fact that 
a mixture has motion and operations as a result of the bodies of which the Mixture is 
composed. But this cannot be said of the things which are present potentially in prime matter. 
And there is also another difference, namely, that even though a mixture is not actually any of 
the mixed bodies which it contains, yet it is something actual. This cannot be said of prime 
matter. But Anaxagoras seems to do away with this difference, because he has not posited any 
particular mixture but the universal mixture of all things. 


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197. The second reason is this: he spoke more subtly than the others, because he came closer 
to a true understanding of the first active principle. For he said that all things are mixed 
together except intellect, and that this alone is unmixed and pure. 

198. From these things it is clear that he posited two principles: one of these he claimed to be 
the intellect itself, insofar as it is simple and unmixed with other things; and the other is prime 
matter, which we claim is like the indeterminate before it is limited and participates in a form. 
For since [prime] matter is [the subject] of an infinite number of forms, it is limited by a form 
and acquires some species by means of it. 

199. It is clear, then, that, in regard to the things which he stated expressly, Anaxagoras 
neither spoke correctly nor clearly. Yet he would seem to say something directly which 
comes closer to the opinions of the later philosophers, which are truer (namely, to those of 
Plato and Aristotle, whose judgments about prime matter were correct) and which were then 
more apparent. 

200. In concluding Aristotle excuses himself from a more diligent investigation of these 
opinions, because the statements of these philosophers belong to the realm of physical 
discussions, which treat of generation and corruption. For these men usually posited 
principles and causes of this 

kind of substance, i.e., of material and corruptible substance. He says "usually," because, 
while they did not treat other substances, certain of the principles laid down by them can also 
be extended to other substances. This is most evident in the case of intellect. Therefore, since 
they have not posited principles common to all substances, which pertains to this science, but 
only principles of corruptible substances, which pertains to the philosophy of nature, a 
diligent study of the foregoing opinions belongs rather to the philosophy of nature than to this 
science. 


LESSON 13 

Criticism of the Pythagoreans' Opinions 
ARISTOTLE'S TEXT Chapters 8 & 9: 989b 24-99oa 34 

98. But all those who make a study of all existing things, and who claim that some are 
sensible and others not, evidently make a study of both classes. And for this reason one 
should dwell at greater length on the statements they have made, whether they be acceptable 
or not, for the purposes of the present study which we now propose to make. 

99. Therefore, those who are called Pythagoreans used principles and elements which are 
foreign to the physicists; and the reason is that they did not take them from sensible things. 
For the objects of mathematics, with the exception of those that pertain to astronomy, are 
devoid of motion. Nevertheless they discuss and treat everything that has to do with the 
physical world; for they generate the heavens and observe what happens in regard to its parts, 
affections and operations. And in doing this they use up their principles and causes, as though 
they agreed with the others, i.e., the physicists, that whatever exists is sensible and is 


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contained by the so-called heavens. But, as we have stated, the causes and principles [of 
which they speak] are sufficient to extend even to a higher class of beings, and are better 
suited to these than to their theories about the physical world. 

100. Yet how there will be motion if only the limited and unlimited and even and odd are 
posited as principles, they do not say. But how can there be generation or corruption, or the 
activities of those bodies which traverse the heavens, if there is no motion or change? 

101. And further, whether one grants them that continuous quantities come from these things, 
or whether this is demonstrated, how is it that some bodies are light and others heavy? For 
from what they suppose and state, they say nothing more about mathematical bodies than they 
do about sensible ones. Hence they have said nothing about fire, earth and other bodies of this 
kind, since they have nothing to say that is proper to sensible things. 

102. Further, how are we to understand that the attributes of number and number itself are 
[the causes] of what exists and comes to pass in the heavens, both from the beginning and 
now? And how are we to understand that there is no other number except that of which the 
world is composed? For when they [place] opportunity and opinion in one part of the 
heavens, and a little above or below them injustice and separation or mixture, and when they 
state as proof of this that each of these is a number, and claim that there already happens to be 
in this place a plurality of quantities constituted [of numbers], because these attributes of 
number correspond to each of these places, [we may ask] whether this number which is in the 
heavens is the same as that which we understand each [sensible] thing to be, or whether there 
is another kind of number in addition to this? For Plato says there is another. In fact, lie also 
thinks that both these things and their causes are numbers, but that some are intellectual 
causes and others sensible ones. 

Chapter 9 

Regarding the Pythagoreans, then, let us dismiss them for the present; for it is enough to have 
touched upon them to the extent that we have. 

COMMENTARY 

201. Here he argues dialectically against the opinions of Pythagoras and Plato, who posited 
different principles than those which pertain to the philosophy of nature. In regard to this he 
does two things. First, he shows that a study of these opinions rather than those mentioned 
above belongs to the present science. Second (202), he begins to argue dialectically against 
these opinions ("Therefore those who"). 

He says, first (98), then, that those who "make a study," i.e., an investigation, of all existing 
things, and hold that some are sensible and others non-sensible, make a study of both classes 
of beings. Hence an investigation of the opinions of those who spoke either correctly or 
incorrectly, belongs rather to the study which we now propose to make in this science. For 
this science deals with all beings and not with some particular class of being. Hence, the 
things which pertain to every class of being are to be considered here rather than those which 
pertain to some particular class of being. 

202. Therefore those who (99). 


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Here he argues against the opinions of the foregoing philosophers. First (99), he argues 
against Pythagoras; and second (208), against Plato ("But those who posited Ideas"). 

In regard to the first he does two things. First, he shows in what way Pythagoras agreed with 
the philosophers of nature, and in what way he differed from them. Second (204), he argues 
against Pythagoras' position ("Yet how"). 

We must understand (99), then, that in one respect the Pythagoreans agreed with the 
philosophers of nature, and in another respect they differed from them. They differed from 
them in their position regarding principles, because they employed principles of things in a 
way foreign to the philosophers of nature. The reason is that they did not take the principles 
of things from sensible beings, as the natural philosophers did, but from the objects of 
mathematics, which are devoid of motion, and are therefore not physical. And the statement 
that the objects of mathematics are devoid of motion must be referred to those sciences which 
are purely mathematical, such as arithmetic and geometry. Astronomy considers motion' 
because astronomy is a science midway between mathematics and natural philosophy. For 
astronomy and the other intermediate sciences apply their principles to natural things, as is 
clear in Book II of the Physics. 

203. Now Pythagoras agreed with the philosophers of nature concerning the things whose 
principles he sought; for he discussed and treated all natural beings. He dealt with the 
generation of the heavens, and observed everything that happens to the parts of the heavens, 
by which are meant the different spheres, or also the different stars. He also considered what 
happens to its affections, or to the eclipses of the luminous bodies; and what happens to the 
operations and motions of the heavenly bodies, and their effects on lower bodies. And he used 
up causes on particular things of this kind by applying to each one its proper cause. He also 
seemed to agree with' the other philosophers of nature in thinking that that alone has being 
which is sensible and is contained by the heavens which we see. For he did not posit an 
infinite sensible body as the other philosophers of nature did. Nor again did he hold that there 
are many worlds, as Democritus did. He therefore seemed to think that there are no beings 
except sensible ones, because he assigned principles and causes only for such substances. 
However, the causes and principles which he laid down are not proper or limited to sensible 
things, but are sufficient for ascending to higher beings, i.e., intellectual ones. And they were 
better fitted to these than the theories of the natural philosophers which could not be extended 
beyond sensible things, because these philosophers claimed that principles are corporeal. But 
since Pythagoras posited incorporeal principles, i.e., numbers, although he only posited 
principles of sensible bodies, he came very close to positing principles of intelligible beings, 
which are not bodies, as Plato did later on. 

204. Yet how (100). 

Here he gives three arguments against the opinion of Pythagoras. The first is this: Pythagoras 
could not explain how motion originates in the world, because he posited as principles only 
the limited and unlimited and the even and odd, which he held to be principles as substance, 
or material principles. But he had to admit that there is motion in the world. For how could 
there be generation and corruption in bodies, and how could there be any activities of the 
heavenly bodies, which occur as a result of certain kinds of motion, unless motion and change 
existed? Evidently they could not exist in any way. Hence, since Pythagoras considered 
generation and corruption and the operations of the heavenly bodies without assigning any 
principle of motion, his position is clearly unsatisfactory. 


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205. And further (101). 

Here he gives the second argument. For Pythagoras claimed that continuous quantities are 
composed of numbers. But whether he proves this or takes it for granted, he could not give 
any reason on the part of numbers as to why some things are heavy and others light. This is 
clear from the fact that his theories about numbers are no more adapted to sensible bodies 
than they are to the objects of mathematics, which are neither heavy nor light. Hence they 
obviously said nothing more about sensible bodies than they did about the objects of 
mathematics. Therefore, since sensible bodies, such as earth and fire and the like, considered 
in themselves, add something over and above the objects of mathematics, it is evident that 
they said nothing proper in any true sense about these sensible bodies. Thus it is also evident 
that the principles which they laid down are not sufficient, since they neglected to give the 
causes of those [attributes] which are proper to sensible bodies. 

206. Further, how are we (102). 

Here he gives the third argument, which is based on the fact that Pythagoras seemed to hold 
two contrary [positions]. For, on the one hand, he held that number and the attributes of 
number arc the cause both of those events which occur in the heavens and of all generable 
and corruptible things from the beginning of the world. Yet, on the other hand, he held that 
there is no other number besides that of which the substance of things is composed; for he 
held that number is the substance of things. But how is this to be understood, since one and 
the same thing is not the cause of itself? For Pythagoras says that the former position may be 
demonstrated from the fact that each one of these sensible things is numerical in substance; 
because in this part of the universe there are contingent beings, about which there is opinion, 
and which are subject to time inasmuch as they sometimes are and sometimes are not. But if 
generable and corruptible things were partly above or partly below, there would be disorder in 
the order of the universe: either after the manner of injustice, i.e., insofar as some being 
would receive a nobler or less noble place than it ought to have; or after the manner of 
separation, i.e., in the sense that, if a body were located outside its own place, it would be 
separated from bodies of a like nature; or after the manner of mixture and mingling, provided 
that a body located outside its proper place must be mixed with some other body, for 
example, if some part of water occupied a place belonging to air or to earth. In this discussion 
he seems to touch on two ways in which a natural body conforms to its proper place: one 
pertains to the order of position, according to which nobler bodies receive a higher place, in 
which there seems to be a kind of justice; and the other pertains to the similarity or 
dissimilarity between bodies in place, to which separation and mingling may be opposed. 
Therefore, insofar as things have a definite position, they are fittingly situated in the universe. 
For if their position were fitting would result, inasmuch as it has been stated and shown that 
all parts of the universe are arranged in a definite proportion; for every definite proportion is 
numerical. And it was from this that Pythagoras showed that all things would be numbers. 
But, on the other hand, we see that the continuous quantities established in different places 
are many and different, because the particular places in the universe correspond to the proper 
attributes by which bodies are differentiated. For the attributes of bodies which are above 
differ from those which are below. Hence, since Pythagoras by means of the above argument 
affirms that all sensible things are numbers, and we see that the difference in sensible bodies 
is attributable to difference in place, the question arises whether the number which exists "in 
the heavens" i.e., in the whole visible body which comprises the heavens, is merely the same 
as that which must be understood to be the substance of each sensible thing, or whether 
besides this number which constitutes the substance of sensible things there is another 
number which is their cause. Now Plato said that there is one kind of number which is the 


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substance of sensible things, and another which is their cause. And while both Plato himself 
and Pythagoras thought that numbers are both sensible bodies themselves and their causes, 
Plato alone considered intellectual numbers to be the causes of things that are not sensible, 
and sensible numbers to be the causes and forms of sensible things. And since Pythagoras did 
not do this, his position is unsatisfactory. 

207. In concluding Aristotle says that these remarks about the Pythagoreans' opinions will 
suffice; for it is enough to have touched upon them to this extent. 


LESSON 14 

Arguments against the Platonic Ideas 
ARISTOTLE'S TEXT Chapter 9: 990a 34-991a 8 

103. But those who posited Ideas, and were the first to seek an understanding of the causes of 
sensible things, introduced other principles equal in number to these — as though one who 
wishes to count things thinks that this cannot be done when they are few, but believes that he 
can count them after he has increased their number. For the separate Forms are almost equal 
to, or not fewer than, these sensible things in the search for whose causes these thinkers have 
proceeded from sensible things to the Forms. For to each thing there corresponds some 
homogeneous entity bearing the same name; and with regard to the substances of other things 
there is a one-in-many, both in the case of these sensible things and in those which are 
eternal. 

104. Furthermore, with regard to the ways in which we Prove that there are Forms, according 
to none of these do they become evident. For from some no syllogism necessarily follows, 
whereas from others there does; and [according to these] there are Forms of things of which 
we do not think there are Forms. 

105. For according to those arguments from [the existence of] the sciences there will be 
Forms of all things of which there are sciences; and according to the argument of the 
one-in-many there will also be Forms of negations. 

106. Again, according to the argument that there is some understanding of corruption, there 
will be Forms of corruptible things; for of these there is some sensible image. 

107. Again, according to the most certain arguments [for the Forms] some establish Forms of 
relations, of which they deny there is any essential class; whereas others lead to "the third 
man." 

108. And in general the arguments for the Forms do away with the existence of the things 
which those who speak of the Forms are more anxious to retain than the Forms themselves. 
For it happens that the dyad [or duality] is not first, but that number is; and that the relative is 
prior to that which exists of itself. And all the other [conclusions] which some [reach] by 
following up the opinions about the Ideas are opposed to the principles [of the theory]. 


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109. Again, according to the opinion whereby we claim that there are Ideas [or Forms], there 
will be Forms not only of substances but also of many other things. For there is one concept 
not only in the case of substances but also in that of other things; and there are sciences not 
only of substance itself but also of other things. And a thousand other such [difficulties] face 
them. 

110. But according to logical necessity and the opinions about the Ideas, if the Forms are 
participated in, there must be Ideas only of substances. For they are not participated in 
according to what is accidental. But things must participate in each Form in this respect: 
insofar as each Form is not predicated of a subject. I mean that if anything participates in 
doubleness itself, it also participates in the eternal, but only accidentally; for it is an accident 
of doubleness to be eternal. Hence the Forms will be substances. 

111. But these things signify substance both here and in the ideal world; [otherwise] why is it 
necessary that a one-in-many appear in addition to these sensible things? Indeed, if the form 
of the Ideas and that of the things which participate in them are the same, there will be 
something in common. For why should duality be one and the same in the case of corruptible 
twos and in those which are many but eternal, rather than in the case of this [Idea of duality] 
and a particular two? But if the form is not the same, there will be pure equivocation; just as if 
one were to call both Callias and a piece of wood man, without observing any common 
attribute which they might have. 

COMMENTARY 

208. Here he argues disputatively against Plato's opinion. This is divided into two parts. First 
(208), he argues against Plato's opinion with reference to his position about the substances of 
things; and second (259), with reference to his position about the principles of things ("And in 
general"). 

The first is divided into two parts. First, he argues against Plato's position that the Forms are 
substances; and second (122:C 239), against the things that he posited about the objects of 
mathematics ("Further, if the Forms"). 

In regard to the first he does two thinks. First, he argues against this position of Plato; and 
second (210), against the reasoning behind it ("Furthermore, with regard to"). 

He says, first (103), that the Platonists, in holding that the Ideas are certain separate 
substances, seemed to be at fault in that, when they sought for the causes of these sensible 
beings, they neglected sensible beings and invented certain other new entities equal in number 
to sensible beings. This seems to be absurd, because one who seeks the causes of certain 
things ought to make these evident and not add other things, the premising of which only adds 
to the number of points which have to be investigated. For it would be similar if a man who 
wished to count certain things which he did not think he was able to count because they are 
few, believed that he could count them by increasing their number through the addition of 
certain other things. But it is evident that such a man has a foolish motive, because the path is 
clearer when there are fewer things; for it is better and easier to make certain of fewer things 
than of many. And the smaller a number is, the more certain it is to us, inasmuch as it is 
nearer to the unit, which is the most accurate measure. And just as the process of counting 
things is the measure we use to make certain of their number, in a similar fashion an 
investigation of the causes of things is the accurate measure for making certain of their 
natures. Therefore, just as the number of fewer numerable things is made certain of more 


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easily, n a similar way the nature of fewer things is made certain of more easily. Hence, when 
Plato increased the classes of beings to the extent that he did with a view to explaining 
sensible things, he added to the number of difficulties by taking what is more difficult in 
order to explain what is less difficult. This is absurd. 

209. That the Ideas are equal in number to, or not fewer than, sensible things, whose causes 
the Platonists seek (and Aristotle includes himself among their number because he was 
Plato's disciple), and which they established by going from sensible things to the aforesaid 
Forms, becomes evident if one considers by what reasoning the Platonists introduced the 
Ideas. Now they reasoned thus: they saw that there is a one-in-many for all things having the 
same name. Hence they claimed that this one-in-many is a Form. Yet with respect to all 
substances of things other than the Ideas we see that there is found to be a one-in-many which 
is predicated of them univocally inasmuch as there are found to be many things which are 
specifically one. This occurs not only in the case of sensible things but also in that of the 
objects of mathematics, which are eternal; because among these there are also many things 
which are specifically one, as was stated above (157). Hence it follows that some Idea 
corresponds to each species of sensible things; and therefore each Idea is something having 
the same name as these sensible things, because the Ideas agree with them in name. For just 
as Socrates is called man, so also is the Idea of man. Yet they differ conceptually; for the 
intelligible structure of Socrates contains matter, whereas that of the ideal man is devoid of 
matter, or, according to another reading, each Form is said to be something having the same 
name [as these sensible things] inasmuch as it is a one-in-many and agrees with the things of 
which it is predicated so far as the intelligible structure of the species is concerned. Hence he 
says that they are equal to, or not fewer than, these things. For either there are held to be Ideas 
only of species, and then they would, be equal in number to these sensible things (granted that 
things are counted here insofar as they differ specifically and not individually, for the latter 
difference is infinite); or there are held to be ideas not only of species but also of genera, and 
then there would be more ideas than there are species of sensible things, because all species 
would be Ideas and in addition to these each and every genus [would be an Idea]. This is why 
he says that they are either not fewer than or more. Or, in another way, they are said to be 
equal inasmuch as he claimed that they are the Forms of sensible things. And he says not 
fewer than but more inasmuch as he held that they are the Forms not only of sensible things 
but also of the objects of mathematics. 

210. Furthermore, with regard to (104). 

Here he argues dialectically against the reasoning behind Plato's position; and in regard to 
this he does two things. First, he gives a general account of the ways in which Plato's 
arguments fail. Second (211), he explains them in detail ("For according to those"). 

He says, first, that with regard to the ways in which we Platonists prove the existence of the 
Forms, according to none of these are the Forms seen to exist. The reason is that "no 
syllogism follows" necessarily from some of these ways, i.e., from certain arguments of Plato, 
because they cannot demonstrate with necessity the existence of the Ideas. However, from 
other arguments a syllogism does follow, although it does not support Plato's thesis; for by 
certain of his arguments there are proved to be Forms of certain things of which the Platonists 
did not think there are Forms, just as there are proved to be Forms of those things of which 
they think there are Forms. 

211. For according to (105). 


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Here he examines in detail the arguments by which the Platonists establish Ideas. First, he 
examines the second argument; and he does this by showing that from Plato's argument it 
follows that there are Forms of some things for which the Platonists did not posit Forms. 
Second (225), he examines the first argument; and he does this by showing that Plato's 
arguments are not sufficient to prove that Ideas exist ("But the most"). 

In regard to the first member of this division he gives seven arguments. The first is this: one 
of the arguments that induced Plato to posit Ideas is taken from scientific knowledge; for 
since science is concerned with necessary things, it cannot be concerned with sensible things, 
which are corruptible, but must be concerned with separate entities which are incorruptible. 
According to the argument taken from the sciences, then, it follows that there are Forms of 
every sort of thing of which there are sciences. Now there are sciences not only of that which 
is one-in-many, which is affirmative, but also of negations; for just as there are some 
demonstrations which conclude with an affirmative proposition, in a similar way there are 
demonstrations which conclude with a negative proposition. Hence it is also necessary to 
posit Ideas of negations. 

212. Again, according to the argument (106). 

Here he gives the second argument. For in the sciences it is not only understood that some 
things always exist in the same way, but also that some things are destroyed; otherwise the 
philosophy of nature, which deals with motion, would be destroyed. Therefore, if there must 
be ideas of all the things which are comprehended in the sciences, there must be Ideas of 
corruptible things as such, i.e., insofar as these are singular sensible things; for thus are things 
corruptible. But according to Plato's theory it cannot be said that those sciences by which we 
understand the processes of corruption in the world attain any understanding of the processes 
of corruption in sensible things; for there is no comprehension of these sensible things, but 
only imagination or phantasy, which is a motion produced by the senses in their act of 
sensing, as is pointed out in The Soul, Book II. 

213. Again, according to the most (107). 

Here he gives the third argument, which contains two conclusions that he says are drawn from 
the most certain arguments of Plato. One conclusion is this: if there are Ideas of all things of 
which there are sciences, and there are sciences not only of absolutes but also of things 
predicated relatively, then in giving this argument it follows that there are also Ideas of 
relations. This is opposed to Plato's view. For, since the separate Ideas are things which exist 
of themselves, which is opposed to the intelligibility of a relation, Plato did not hold that there 
is a class of Ideas of relations, because the Ideas are said to exist of themselves. 

214. The second conclusion is one which follows from other most certain arguments, namely, 
that there is "a third man." This phrase can be understood in three ways. First, it can mean 
that the ideal man is a third man distinct from two men perceived by the senses, who have the 
common name man predicated of both of them. But this does not seem to be what he has in 
mind, even though it is not mentioned in the Sophistical Refutations, Book II; for this is the 
position against which he argues. Hence according to this it would not lead to an absurdity. 

215. The second way in which this expression can be understood is this: the third man means 
one that is common to the ideal man and to one perceived by the senses. For since both a man 
perceived by the senses and the ideal man have a common intelligible structure, like two men 
perceived by the senses, then just as the ideal man is held to be a third man in addition to two 


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men perceived by the senses, in a similar way there should be held to be another third man in 
addition to the ideal man and one perceived by the senses. But neither does this seem to be 
what he has in mind here, because he leads us immediately to this absurdity by means of 
another argument. Hence it would be pointless to lead us to the same absurdity here. 

216. The third way in which this expression can be understood is this: Plato posited three 
kinds of entities in certain classes of things, namely, sensible substances, the objects of 
mathematics and the Forms. He does this, for example, in the case of numbers, lines and the 
like. But there is no reason why intermediate things should be held to exist in certain classes 
rather than in others. Hence in the class of man it was also necessary to posit an intermediate 
man, who will be a third man midway between the man perceived by the senses and the ideal 
man. Aristotle also gives this argument in the later books of this work (2160). 

217. And in general (108). 

Here he gives the fourth argument, which runs as follows. Whoever by his own reason he 
does away with certain [principles] which are better known to him than the ones which he 
posits, adopts an absurd position. But these theories about the Forms which Plato held do 
away with certain principles whose reality the Platonists (when they said that there are Ideas) 
were more convinced of than the existence of the Ideas. Therefore Plato's position is absurd. 
The minor premise is proved in this way. According to Plato the Ideas are prior both to 
sensible things and to the objects of mathematics. But according to him the Ideas themselves 
are numbers; and they are odd numbers rather than even ones, because he attributed odd 
number to form and even number to matter. Hence he also said that the dyad [or duality] is 
matter. Therefore it follows that other numbers are prior to the dyad, which he held to be the 
matter of sensible things, and identified with the great and small. Yet the Platonists asserted 
the very opposite of this, that is to say, that the dyad is first in the class of number. 

218. Again, if, as has been proved by the above argument (213), there must be Ideas of 
relations, which are self-subsistent relations, and if the Idea itself is prior to whatever 
participates in the Idea, it follows that the relative is prior to the absolute, which is said to 
exist of itself. For sensible substances of this kind, which participate in Ideas, are said to be in 
an unqualified sense. And in like manner whatever those who follow the opinion about the 
Ideas say of all things is opposed to self-evident principles which even they themselves are 
most ready to acknowledge. 

219. Again, according to the opinion (109). 

Here he gives the fifth argument, which is as follows: Ideas were posited by Plato in order 
that the intelligible structures and definitions of things given in the sciences might correspond 
to them, and in order that there could be sciences of them. But there is "one concept," i.e., a 
simple and indivisible concept, by which the quiddity of each thing is known, i.e., not only 
the quiddity of substances "but also of other things," namely, of accidents. And in a similar 
way there are sciences not only of substance and about substance, but there are also found to 
be sciences "of other things," i.e., of accidents. Hence according to the opinion by which you 
Platonists acknowledge the existence of Ideas, it evidently follows that there will be Forms 
not only of substances but also of other things, i.e., of accidents. This same conclusion 
follows not only because of definitions and the sciences, but there also happen to be many 
"other such" [reasons], i.e., very many .reasons why it is necessary to posit Ideas of accidents 
according to Plato's arguments. For example, he held that the Ideas are the principles of being 
and of becoming in the world, and of many such aspects which apply to accidents. 


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220. But, on the other hand, according to Plato's opinion about the Ideas and according to 
logical necessity, insofar as the Ideas are indispensable to sensible things, i.e., "insofar" s as 
they are capable of being participated in by sensible things, it is necessary to posit Ideas only 
of substances. This is proved thus: things which are accidental are not participated in. But an 
Idea must be participated in by each thing insofar as it is not predicated of a subject. This 
becomes clear as follows: if any sensible thing participates in "doubleness itself," i.e., in a 
separate doubleness (for Plato spoke of all separated things in this way, namely, as 
self-subsisting things), it must participate in the eternal. But it does not do this essentially 
(because then it would follow that any double perceived by the senses would be eternal), but 
accidentally, i.e., insofar as doubleness itself, which is participated in, is eternal. And from 
this it is evident that there is no participation in things which are accidental, but only in 
substances. Hence according to Plato's position a separate Form was not an accident but only 
a substance. Yet according to the argument taken from the sciences there must also be Forms 
of accidents, as was stated above (219). 

221. But these things (111). 

Then he gives the sixth argument, which runs thus: these sensible things signify substance 
both in the case of things perceived by the senses and in that of those in the ideal world, i.e., 
in the case of intelligible things, which signify substance; because they held that both 
intelligible things and sensible ones are substance. Therefore it is necessary to posit in 
addition to both of these substances — intelligible and sensible ones — some common entity 
which is a one-in-many. For the Platonists maintained that the Ideas exist on the grounds that 
they found a one-in-many which they believed to be separate from the many. 

222. The need for positing a one apart from both sensible substances and the Forms he proves 
thus: the Ideas and the sensible things which participate in them either belong to one class or 
not. If they belong to one class, and it is necessary to posit, according to Plato's position, one 
common separate Form for all things having a common nature, then it will be necessary to 
Posit some entity common to both sensible things and the Ideas themselves) which exists 
apart from both. Now one cannot answer this argument by saying that the Ideas, which are 
incorporeal and immaterial, do not stand in need of any higher Forms; because the objects of 
mathematics, which Plato places midway between sensible substances and the Forms, are 
similarly incorporeal and immaterial. Yet since many of them are found to belong to one 
species, Plato held that there is a common Form for these things, in which not only the objects 
of mathematics participate but also sensible substances. Therefore, if the twoness [or duality] 
which is the Form or Idea of twoness is identical with that found in sensible twos, which are 
corruptible (just as a pattern is found in the things fashioned after it), and with that found in 
mathematical twos, which are many in one class (but are nevertheless eternal) ' then for the 
same reason in the case of the same twoness, i.e., the Idea two , and in that of the other 
twoness, which is either mathematical or sensible, there will be another separate twoness. For 
no reason can be given why the former should exist and the latter should not. 

223. But if the other alternative is admitted — that sensible things, which participate in the 
Ideas, do not have the same form as the Ideas — it follows that the name which is predicated of 
both the Ideas and sensible substances is predicated in a purely equivocal way. For those 
things are said to be equivocal which have only a common name and differ in their intelligible 
structure. And it follows that they are not only equivocal in every way but equivocal in an 
absolute sense, like those things on which one name is imposed without regard for any 
common attribute, which are said to be equivocal by chance; for example, if one were to call 
both Callias and a piece of wood man. 


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224. Now Aristotle added this because someone might say that a name is not predicated of an 
Idea and of a sensible substance in a purely equivocal way, since a name is predicated of an 
Idea essentially and of a sensible substance by participation. For, according to Plato, the Idea 
of man is called "man in himself," whereas this man whom we apprehend by the senses is 
said to be a man by participation. However, such an equivocation is not pure equivocation. 
But a name which is predicated by participation is predicated with reference to something that 
is predicated essentially; and this is not pure equivocation but the multiplicity of analogy. 
However, if an Idea and a sensible substance were altogether equivocal by chance, it would 
follow that one could not be known through the other, as one equivocal thing cannot be 
known through another. 


LESSON 15 

The Destruction of the Platonists' Arguments for Ideas 
ARISTOTLE'S TEXT Chapter 9: 991a 8-991b 9 

112. But the most important problem of all that one might raise is what the Forms contribute 
to sensible things, either to those which are eternal or to those which are generated and 
corrupted. 

113. For they are not the cause of motion or of any change whatever in these things. 

114. Nor are they of any assistance in knowing other things; for they are not the substance of 
other things, because if they were they would exist in them. Nor do they contribute anything 
to the being of other things; for they are not present in the things which participate in them. 
For if they were they would perhaps seem to be causes, as whiteness mixed with some white 
thing. But this theory, which was first stated by Anaxagoras and later by Hesiod and certain 
other thinkers, is easily disposed of. For it is easy to bring many absurd conclusions against 
such a view. In fact other things are not derived from the Forms in any of the customary 
senses. 

115. Again, to say that they are exemplars, and that other things participate in them, is to 
speak with empty talk and to utter poetic metaphors. 

116. For what is the work which looks towards the Ideas [as an exemplar]? For one thing may 
both be and become similar to another thing and not be made in likeness to it. So whether 
Socrates exists or not, a man such as Socrates might come to be. 

117. Similarly, it is evident that this will be the case even if Socrates is eternal. And there will 
be many exemplars of the same thing, and for this reason many Forms, as animal and 
two-footed and man-in-himself will be the Form of man. 

118. Further, the Forms will be the exemplars not only of sensible things but also of the 
Forms themselves, as the genus of the species. Hence the same thing will be both an exemplar 
and a copy. 


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19. Again, it is thought to be impossible that the substance of a thing and that of which it is 
the substance should exist apart. Hence, if the Forms are the substances of things, how will 
they exist apart from them? 

120. But in the Phaedo it is stated that the Forms are the causes both of being and of coming 
to be. Yet even if the Forms do exist, still the things which participate in them will not come 
to be unless there is something which produces motion. 

121. And many other things come to be, such as a house and a ring, of which we do not say 
that there are any Forms. It is evident, then, that other things can exist and come to be because 
of such causes as those [responsible for the things] just mentioned. 

COMMENTARY 

225. Here Aristotle attacks the opinion of Plato insofar as he did not draw the conclusion 
which he intended to draw. For Plato intended to conclude that there are Ideas by this 
argument that they are necessary in some way for sensible things. Hence, Aristotle, by 
showing that the Ideas cannot contribute anything to sensible things, destroys the arguments 
by which Plato posits Ideas. Thus he says (112) that of all the objections which may be raised 
against Plato the foremost is that the Forms which Plato posited do not seem to contribute 
anything to sensible things, either to those which are eternal, as the celestial bodies, or to 
those which are generated and corrupted, as the elemental bodies. He shows (113) that this 
criticism applies to each of the arguments by which Plato posited Ideas ("For they are not"). 

226. At this point in the text (113) he begins to present his five objections [against the 
Platonic arguments for Ideas] . 

He argues, first (226), that they are useless in explaining motion; second (227), that they are 
use 

less in explaining our knowledge of sensible things ("Nor are they"); third (231), that they are 
of no value as exemplars ("Again, to say"); fourth (236), that they are of no value as the 
substances of things ("Again, it is thought"); and fifth (237) that they are of no value as 
causes of generation ("But in the Phaedo"). 

Accordingly, he says, first (113), that the Forms cannot contribute anything to sensible things 
in such a way as to be the cause of motion or of any kind of change in them. He does not give 
the reason for this here but mentioned it above (237), because it is clear that the Ideas were 
not introduced to explain motion but rather to explain immutability. For since it seemed to 
Plato that all sensible things are always in motion, he wanted to posit something separate 
from sensible things that is fixed and immobile, of which there can be certain knowledge. 
Hence, according to him, the Forms could not be held to be sensible principles of motion, but 
rather to be immutable things and principles of immutability; so that, undoubtedly, whatever 
is found to be fixed and constant in sensible things will be due to participation in the Ideas, 
which are immutable in themselves. 

227. Nor are they of any assistance (1 14). 

Second, he shows that the Forms do not contribute anything to the knowledge of sensible 
things, by the following argument: knowledge of each thing is acquired by knowing its own 
substance, and not by knowing certain substances which are separate from it. But these 


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separate substances, which they call Forms, are altogether othef than sensible substances. 
Therefore a knowledge of them is of no assistance in knowing other sensible things. 

228. Nor can it be said that the Forms are the substances of these sensible things; for the 
substance of each thing is present in the thing whom substance it is. Therefore, if then Forms 
were the substances of sensible things, they would be present in sensible things. This is 
opposed to Plato's opinion. 

229. Nor again can it be said that the Forms are present in these sensible substances as in 
things which participate in them; for Plato thought that some Forms are the causes of sensible 
things in this way. For just as we might understand whiteness itself existing of itself as a 
certain separate whiteness to be mingled with the whiteness in a subject, and to participate in 
whiteness, in a similar way we . might say that man [in himself], who is separate, is mingled 
with this man who is composed of matter and the specific nature in which he participates. But 
this argument is easily "disposed of, ' i.e., destroyed; for Anaxagoras, who also held that 
forms and accidents are mingled with things, was the first to state it. Hesiod and certain other 
thinkers were the second to mention it. Therefore I say that it is easily disposed of, because it 
is easy to bring many absurd conclusions against such an opinion. For it would follow as he 
pointed out above (194) against Anaxagoras, that accidents and forms could exist without 
substances. For only those things can exist separately which are naturally disposed to be 
mixed with other things. 

230. It cannot be said, then, that the Forms contribute in any way to our knowledge of 
sensible things as their substances. Nor can it be said that they are the principles of being in 
these substances by way of participation. Nor again can it be said that from these Forms as 
principles other things — sensible ones — come to be in any of the ways in which we are 
accustomed to 

speak. Therefore, if principles of being and principles of knowledge are the same, the Forms 
cannot possibly make any contribution to scientific knowledge, since they cannot be 
principles of lwing. Hence he says "in any of the customary ways" of speaking, because 
Plato invented many new ways of deriving knowledge of one thing from something else. 

231. Again, to say (115). 

Here he gives the third objection against the arguments for separate Forms. He says that the 
Forms are of no value to sensible things as their exemplars. First (115), he states his thesis; 
and, second (232), he proves it ("For what is the work"). 

Accordingly he says, first (1 15), that to say that the Forms are the exemplars both of sensible 
things and the objects of mathematics (because the latter participate in causes of this kind), is 
untenable for two reasons. First, because it is vain and useless to posit exemplars of this kind, 
as he will show; and second, because this manner of speaking is similar to the metaphors 
which the poets introduce, which do not pertain to the philosopher. For the philosopher ought 
to teach by using proper causes. Hence he says that this manner of speaking is metaphorical, 
because Plato likened the generation of natural substances to the making of works of art, in 
which the artisan, by looking at some exemplar, produces something similar to his artistic 
idea. 

232. For what is the work (116). 


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Here he proves his thesis by three arguments. For the work, i.e., the use, of an exemplar, 
seems to be this, that the artisan by looking at an exemplar induces a likeness of the form in 
his own artifact. But in the operations of natural beings we see that like things are generated 
by like, as man is generated by man. Therefore this likeness arises in things which are 
generated, either because some agent looks toward an exemplar or not. If not, then what is 
"the work," or utility, of the agent's so looking toward the Ideas as exemplars? — as if to say, 
none. But if the likeness results from looking at a separate exemplar, then it cannot be said 
that the cause of this likeness in the thing generated is the form of an inferior agent. For 
something similar would come into being with reference to this separate exemplar and not 
with reference to this sensible agent. And this is what he means when he says "and not be like 
it," i.e., like the sensible agent. From this the following absurdity results: someone similar to 
Socrates will be generated whether Socrates is held to exist or not. This we see is false; for 
unless Socrates plays an active part in the process of generation, no one similar to Socrates 
will ever be generated. Therefore, if it is false that the likeness of things which are generated 
does not depend on proximate agents, it is pointless and superfluous to posit separate 
exemplars of any kind. 

233. However, it should be noted that, even though this argument does away with the separate 
exemplars postulated by Plato, it still does not do away with the fact that God's knowledge is 
the exemplar of all things. For since things in the physical world are naturally inclined to 
induce their likeness in things which are generated, this inclination must be traced back to 
some directing principle which ordains each thing to its end. This can only be the intellect of 
that being who knows the end and the relationship of things to the end. Therefore this likeness 
of effects to their natural causes is traced back to an intellect as their first principle. But it is 
not necessary that this likeness should be traced back to any other separate forms; because in 
order to have the above-mentioned likeness this direction of things to their end, according to 
which natural powers are directed by the first intellect, is sufficient. 

234. Similarly, it is evident (117). 

Here he gives the second argument, which runs as follows: just as Socrates because he is 
Socrates adds something to man, in a similar way man adds something to animal. And just as 
Socrates participates in man, so does man participate in animal. But if besides this Socrates 
whom we perceive there is held to be another Socrates who is eternal, as his exemplar, it will 
follow that there are several exemplars of this Socrates whom we perceive, i.e., the eternal 
Socrates and the Form man. And by the same reasoning the Form man will have several 
exemplars; for its exemplar will be both animal and two-footed and also "man-in-himself," 
i.e., the Idea of man. But that there should be several exemplars of a single thing made in 
likeness to an exemplar is untenable. Therefore it is absurd to hold that things of this kind are 
the exemplars of sensible things. 

235. Further (118). 

Here he gives the third argument, which runs thus: just as a Form is related to an individual, 
so also is a genus related to a species. Therefore, if the Forms are the exemplars of individual 
sensible things, as Plato held, there will be also certain exemplars of these Forms, that is to 
say, their genus. But this is absurd, because then it would follow that one and the same thing, 
i.e., Form, would be an exemplar of one thing, namely, of the individual whom we perceive 
by the senses, and a copy made in likeness to something else, namely, a genus. This seems to 
be absurd. 


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236. Again, it is thought (119). 

Here he proves his fourth objection, namely, that the Forms contribute nothing to sensible 
things as their substances or formal causes; because "It is thought by him," that is to say, it is 
a matter of opinion (to put this impersonally), that it is impossible for a thing's substance to 
exist apart from the thing whose substance it is. But the Forms exist apart from the things of 
which they are the Forms, i.e., apart, from sensible things. Therefore they are not the 
substances of sensible things. 

237. But in the "Phaedo" (120). 

Here he shows that the Forms are of no value in accounting for the coming to be of sensible 
things, although Plato said "in the Phaedo," i.e., in one of his works, that the Forms are the 
causes both of the being and of the coming to be of sensible things. 

But Aristotle disproves this by two arguments. The first is as follows: to posit the cause is to 
posit the effect. However, even if the Forms exist, the particular or individual things which 
participate in the Forms will come into being only if there is some agent which moves them to 
acquire form. This is evident from Plato's opinion that the Forms are always in the same state. 
Therefore, assuming that these Forms exist, if individuals were to exist or come into being by 
participating in them, it would follow that individual substances of this kind would always be. 
This is clearly false. Therefore it cannot be said that the Forms are the causes of both the 
coming to be and the being of sensible things. The chief reason is that Plato did not hold that 
the Forms are efficient causes, as was stated above (226). For Aristotle holds that the being 
and coming to be of lower substances proceeds from immobile separate substances, inasmuch 
as these substances are the movers of the celestial bodies, by means of which generation and 
corruption are produced in these lower substances. 

238. And many other (121). 

Here he gives the second argument, which runs thus: just as artifacts are related to artificial 
causes, so are natural bodies to natural causes. But we see that many other things besides 
natural bodies come into being in the realm of these lower bodies, as a house and a ring, for 
which the Platonists did not posit any Forms. Therefore "other things," namely, natural 
things, can both be and come to be because of such proximate causes as those just mentioned, 
i.e., artificial ones; so that, just as artificial things come to be as a result of proximate agents, 
so also do natural things. 


LESSON 16 

Arguments against the View that Ideas Are Numbers 
ARISTOTLE'S TEXT Chapter 9: 991b 9-992a 24 

122. Further, if the Forms are numbers, in what way will they be causes? Will it be because 
existing things are other numbers, so that this number is man, another Socrates, and still 
another Callias? In what respect, then, are the former the cause of the latter? For it will make 
no difference if the former are eternal and the latter are not. But if it is because the things here 


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are ratios of numbers, like a harmony, then clearly there will be one kind of thing of which 
they are the ratios. And if this is matter, evidently the numbers themselves will be certain 
ratios of one thing to something else. I mean that, if Callias is a numerical ratio of fire, water, 
earth and air, [his Idea will also be a ratio of certain things], and man-in-himself, whether it 
be a number or not, will still be a numerical ratio of certain things and not just a number; nor 
will it be any number because of these. 

123. Again, one number will come from many numbers, but how or in what way can one 
Form come from [many] Forms? 

124. But if one number is not produced from them but from the units which they contain, as 
the units in the number ten thousand, how are the units related? For if they are specifically the 
same, many absurdities will follow; and if they are not, neither will they be the same as one 
another nor all the others the same as all. 

125. For in what way Will they differ, if they have no attributes? For these statements are 
neither reasonable nor in accord with our understanding. 

126. Further, [if the Forms are numbers], it is necessary to set up some other class of number: 
that with which arithmetic deals. And all the things which an said to be intermediate, from 
what things or what principles in an absolute sense will they come, or why will they be [an 
intermediate class] between a the things at hand and those [in the ideal world]? 

127. Again, each of the units which are contained in the number two will come from a prior 
two. But this is impossible. 

128. Further, why is a number something composed of these? 

129. And, again, in addition to what has been said, if the units are different, it will be 
necessary to speak of them in the same way as do those who say that the elements are four or 
two. For none of them designate as an element what is common, namely, body, but fire and 
earth, whether body is something in common or not. But now we are speaking of the one as if 
it were one thing made up of like parts, as fire or water. But if this is the case, numbers will 
not be substances. Yet it is evident that, if the one itself is something common and a principle, 
then the one is used in different senses; otherwise this will be impossible. 

130. Now when we wish to reduce substances to their principles, we claim that lengths come 
from the long and short, i.e., from a kind of great and small; and the plane from the wide and 
narrow; and body from the deep and shallow. 

131. Yet how will a surface contain a line, or a solid a line or surface? For the wide and 
narrow is a different class from the deep and shallow. Hence, just as number is not present in 
these, because the many and few differ from these, it is evident that no one of the other higher 
classes will be present in the lower. And the broad is not in the class of the deep, for then the 
solid would be a kind of surface. 

132. Further, from what will points derive being? Plato was opposed to this class of objects as 
a geometrical fiction, but he called them the principle of a line. And he often holds that there 
are indivisible lines. Yet these must have some [limit]. Therefore any argument that proves 
the existence of the line also proves the existence of the point. 


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COMMENTARY 

239. Here he destroys Plato's opinion about the Forms inasmuch as Plato claimed that they 
are numbers. In regard to this he does two things. First, he argues dialectically against Plato's 
opinion about numbers, and second (254), against his opinion about the other objects of 
mathematics ("Now when we wish"). 

In regard to the first part he gives six arguments. The first (122) is this: in the case of things 
which are substantially the same, one thing is not the cause of another. But sensible things are 
substantially numbers according to the Platonists and Pythagoreans. Therefore, if the Forms 
themselves are numbers, they cannot be the cause of sensible things. 

240. But if it is said that some numbers are Forms and others are sensible filings, as Plato 
literally held (as though We were to say that this number is man and another is Socrates and 
still another is Callias), even this would not seem to be sufficient; for according to this view 
the intelligible structure of number will be common both to sensible things and the Forms. 
But in the case of things which have the same intelligible structure, one does not seem to be 
the cause of another. Therefore the Forms will not be the causes of sensible things. 

241. Nor again can it be said that they are causes for the reason that, if those numbers are 
Forms, they are eternal. For this difference, namely, that some things differ from others in 
virtue of being eternal and non-eternal in their own being considered absolutely, is not 
sufficient to explain why some things are held to be the causes of others. Indeed, things differ 
from each other as cause and effect rather because of the relationship which one has to the 
other. Therefore things that differ numerically do not differ from each other as cause and 
effect because some are eternal and some are not. 

242. Again, it is said that sensible things are certain "ratios" or proportions of numbers, and 
that numbers are the causes of these sensible things, as we also observe to be the case "in 
harmonies," i.e., in the combinations of musical notes. For numbers are said to be the causes 
of harmonies insofar as the numerical proportions applied to sounds yield harmonies. Now if 
the above is true, then just as in harmonies there are found to be sounds in addition to 
numerical proportions, in a similar way it was obviously necessary to posit in addition to the 
numbers in sensible things something generically one to which the numerical proportions are 
applied, so that the proportions of those things which belong to that one genus would 
constitute sensible things. However, if that to which the numerical proportion in sensible 
things is applied is matter, evidently those separate numbers, which are Forms, had to be 
termed proportions of some one thing to something else. For this particular man, called 
Callias or Socrates, must be said to be similar to the ideal man, called "man-in-himself," or 
humanity. Hence, if Callias is not merely a number, but is rather a kind of ratio or numerical 
proportion of the elements, i.e., of fire, earth, water and air, and if the ideal man-in-himself is 
a kind of ratio or numerical proportion of certain things, the ideal man will not be a number 
by reason of its own substance. From this it follows that there will be no number "apart from 
these," i.e., apart from the things numbered. For if the number which constitutes the Forms is 
separate in the highest degree, and if it is not separate from things but is a kind of proportion 
of numbered things, no other number will now be separate. This is opposed to Plato's view. 

243. It also follows that the ideal man is a proportion of certain numbered things, whether it is 
held to be a number or not. For according to those who held that substances are numbers, and 
according to the philosophers of nature, who denied that numbers are substances, some 
numerical proportions must be found in the substances of things. This is most evident in the 


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case of the opinion of Empedocles, who held that each one of these sensible things is 
composed of a certain harmony or proportion [of the elements]. 

244. Again, one number (123). 

Here he gives the second argument which runs thus: one number is produced from many 
numbers. Therefore, if the Forms are numbers, one Form is produced from many Forms. But 
this is impossible. For if from many things which differ specifically something specifically 
one is produced, this comes about by mixture, in which the natures of the things mixed are 
not preserved; just as a stone is produced from the four elements. Again, from things of this 
kind which differ specifically one thing is not produced by reason of the Forms, because the 
Forms themselves are combined in such a way as to constitute a single thing only in 
accordance with the intelligible structure of individual things, which are altered in such a way 
that they can be mixed together. And when the Forms themselves of the numbers two and 
three are combined, they give rise to the number five, so that each number remains and is 
retained in the number five. 

245. But since someone could answer this argument, in support of Plato, by saying that one 
number does not come from many numbers, but each number is immediately constituted of 
units, Aristotle is therefore logical in rejecting this answer (124) ("But if one number"). 

For if it is said that some greater number, such as ten thousand, is not produced "from them," 
namely, from twos or many smaller numbers, but from "units," i.e., ones, this question will 
follow: How are the units of which numbers are composed related to each other? For all units 
must either conform with each other or not. 

246. But many absurd conclusions follow from the first alternative, especially for those who 
claim that the Forms are numbers. For it will follow that different Forms do not differ 
substantially but only insofar as one Form surpasses another. It also seems absurd that units 
should differ in no way and yet be many, since difference is a result of multiplicity. 

247. But if they do not conform, this can happen in two ways. First, they can lack conformity 
because the units of one number differ from those of another number, as the units of the 
number two differ from those of the number three, although the units of one and the same 
number will conform with each other. Second, they can lack conformity insofar as the units of 
one and the same number do not conform with each other or with the units of another number. 
He indicates this distinction when he says, "For neither will they be the same as one another 
(125)," i.e., the units which comprise the same number, "nor all the others the same as all," 
i.e., those which belong to different numbers. Indeed, in whatever way there is held to be lack 
of conformity between units an absurdity is apparent. For every instance of non-conformity 
involves some form or attribute, just as we see that bodies which lack conformity differ 
insofar as they are hot and cold, white and black, or in terms of similar attributes. Now units 
lack qualities of this kind, because they have no qualities, according to Plato. Hence it will be 
impossible to hold that there is any non-conformity or difference between them of the kind 
caused by a quality. Thus it is evident that Plato's opinions about the Forms and numbers are 
neither "reasonable" (for example, those proved by an apodictic argument), nor "in accord 
with our understanding" (for example, those things which are self-evident and verified by [the 
habit of] intellect alone, as the first principles of demonstration). 

248. Further, [if the Forms] (126). 


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Here he gives the third argument against Plato, which runs thus: all objects of mathematics, 
which Plato affirmed to be midway between the Forms and sensible substances, are derived 
unqualifiedly from numbers, either as proper principles, or as first principles. He says this 
because in one sense numbers seem to be the immediate principles of the other objects of 
mathematics; for the Platonists said that the number one constitutes the point, the number two 
the line, the number three surface, and the number four the solid. But in another sense the 
objects of mathematics seem to be reduced to numbers as first principles and not as proximate 
ones. For the Platonists said that solids are composed of surfaces, surfaces of lines, lines of 
points, and points of units, which constitute numbers. But in either way it followed that 
numbers are the principles of the other objects of mathematics. 

249. Therefore, just as the other objects of mathematics constituted an intermediate class 
between sensible substances and the Forms, in a similar way it was necessary to devise some 
class of number which is other than the numbers that constitute the Forms and other than 
those that constitute the substance of sensible things. And arithmetic, which is one of the 
mathematical sciences, evidently deals with this kind of number as its proper subject, just as 
geometry deals with mathematical extensions. However, this position seems to be 
superfluous; for no reason can be given why number should be midway "between the things 
at hand," or sensible things, and "those in the ideal world," or the Forms, since both sensible 
things and the Forms are numbers. 

250. Again, each of the units (127). 

Here he gives the fourth argument, which runs thus: those things which exist in the sensible 
world and those which exist in the realm of mathematical entities are caused by the Forms. 
Therefore, if some number two is found both in the sensible world and in the realm of the 
objects of mathematics, each unit of this subsequent two must be caused by a prior two, 
which is the Form of twoness. But it is "impossible" that unity should be caused by duality. 
For it would be most necessary to say this if the units of one number were of a different 
species than those of another number, because then these units would acquire their species 
from a Form which is prior to the units of that number. And thus the units of a subsequent two 
would have to be produced from a prior two. 

251. Further, why is (128). 

Here he gives the fifth argument, which runs thus: many things combine so as to constitute 
one thing only by reason of some cause, which can be considered to be either extrinsic, as 
some agent which unites them, or intrinsic, as some unifying bond. Or if some things are 
united of themselves, one of them must be potential and another actual. However, in the case 
of units none of these reasons can be said to be the one "why a number," i.e., the cause by 
which a number, will be a certain "combination," ' i.e., collection of many units; as if to say, 
it will be impossible to give any reason for this. 

252. And, again, in addition (129). 

Here he gives the sixth argument, which runs thus: if numbers are the Forms and substances 
of things, it will be necessary to say, as has been stated before (245), either that units are 
different, or that they conform. But if they are different, it follows that unity as unity will not 
be a principle. 


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This is clarified by a similar case drawn from the position of the natural philosophers. For 
some of these thinkers held that the four [elemental] bodies are principles. But even though 
being a body is common to these elements, these philosophers did not maintain that a 
common body is a principle, but rather fire, earth, water and air, which are different bodies. 
Therefore, if units are different, even though all have in common the intelligible constitution 
of unity, it will not be said that unity itself as such is a principle. This is contrary to the 
Platonists' position; for they now say that the unit is the principle of things, just as the natural 
philosophers say that fire or water or some body with like parts is the principle of things. But 
if our conclusion against the Platonists' theory is true-that unity as such is not the principle 
and substance of things-it will follow that numbers are not the substances of things. For 
number is held to be the substance of things only insofar as it is constituted of units, which 
are said to be the substances of things. This is also contrary to the Platonists' position which 
is now being examined, i.e., that numbers are Forms. 

253. But if you say that all units are undifferentiated, it follows that "the whole," i.e., the 
entire universe, is a single entity, since the substance of each thing is the one itself, and this is 
something common and undifferentiated. Further, it follows that the same entity is the 
principle of all things. But this is impossible by reason of the notion involved, which is 
inconceivable in itself, namely, that all things should be one according to the aspect of 
substance. For this view contains a contradiction, since it claims that the one is the substance 
of all things, yet maintains that the one is a principle. For one and the same thing is not its 
own principle, unless, perhaps, it is said that "the one" is used in different senses, so that 
when the senses of the one are differentiated all things are said to be generically one and not 
numerically or specifically one. 

254. Now when we wish (130). 

Here he argues against Plato's position with reference to his views about mathematical 
extensions. First (130), he gives Plato's position; and second (255), he advances an argument 
against it ("Yet how will"). 

He says, first, that the Platonists, wishing to reduce the substances of things to their first 
principles, when they say that continuous quantities themselves are the substances of sensible 
things, thought they had discovered the principles of things when they assigned line, surface 
and solid as the principles of sensible things. But in giving the principles of continuous 
quantities they said that "lengths," i.e., lines, are composed of the long and short, because 
they held that contraries are the principles of all things. And since the line is the first of 
continuous quantities, they first attributed to it the great and small; for inasmuch as these two 
are the principles of the line, they are also the principles of other continuous quantities. He 
says "from the great and small" because the great and small are also placed among the Forms, 
as has been stated (217). But insofar as they are limited by position, and are thus 
particularized in the class of continuous quantities, they constitute first the line and then other 
continuous quantities. And for the same reason they said that surface is composed of the wide 
and narrow, and body of the deep and shallow. 

255. Yet how will a surface (130). 

Here he argues against the foregoing position, by means of two arguments. The first is as 
follows. Things whose principles are different are themselves different. But the principles of 
continuous quantities mentioned above are different, according to the foregoing position, for 
the wide and narrow, which are posited as the principles of surface, belong to a different class 


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than the deep and shallow, which are held to be the principles of body. The same thing can be 
said of the long and short, which differ from each of the above. Therefore, line, surface and 
body all differ from each other. How then will one be able to say that a surface contains a 
line, and a body a line and a surface? In confirmation of this argument he introduces a similar 
case involving number. For the many and few, which are held to be principles of things for a 
similar reason, belong to a different class than the long and short, the wide and narrow, and 
the deep and shallow. Therefore number is not contained in these continuous quantities but is 
essentially separate. Hence, for the same reason, the higher of the above mentioned things 
will not be contained in the lower; for example, a line will not be contained in a surface or a 
surface in a body. 

256. But because it could be said that certain of the foregoing contraries are the genera of the 
others, for example, that the long is the genus of the broad, and the broad the genus of the 
deep, he destroys this [objection] by the following argument: things composed of principles 
are related to each other in the same way as their principles are. Therefore, if the broad is the 
genus of the deep, surface will also be the genus of body. Hence a solid will be a kind of 
plane, i.e., a species of surface. This is clearly false. 

257. Further, from what will (132). 

Here he gives the second argument, which involves points; and in regard to this Plato seems 
to have made two errors. First, Plato claimed that a point is the limit of a line, just as a line is 
the limit of a surface and a surface the limit of a body. Therefore, just as he posited certain 
principles of, which the latter are composed, so too he should have posited some principle 
from which points derive their being. But he seems to have omitted this. 

258. The second error is this: Plato seems to have held different opinions about points. For 
sometimes he maintained that the whole science of geometry treats this class of things, 
namely, points, inasmuch as he held that points are the principles and substance of all 
continuous quantities. And he not only implied this but even explicitly stated that a point is 
the principle of a line, defining it in this way. But many times he said that indivisible lines are 
the principles of lines and other continuous quantities, and that this is the class of things with 
which geometry deals, namely, indivisible lines. Yet by reason of the fact that he held that all 
continuous (quantities are composed of indivisible lines, he did not avoid the consequence 
that continuous quantities are composed of points, and that points are the principles of 
continuous quantities. For indivisible lines must have some limits, and these can only be 
points. Hence, by whatever argument indivisible lines are held to be the principles of 
continuous quantities, by the same argument too the point is held to be the principle of 
continuous quantity. 


LESSON 17 

Arguments against the View that the Ideas Are Principles of Being and Knowledge 
ARISTOTLE'S TEXT Chapters 9 & 10: 992a 24-993a 27 

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133. And, in general, even though wisdom investigates the causes of apparent things, we have 
neglected this study. For we say nothing about the cause from which motion originates. And 
while we think that we are stating the substance of these sensible things, we introduce other 
substances. But the way in which we explain how the latter are the substances of the former is 
empty talk; for to participate, as we have said before (115), signifies nothing. Moreover, that 
which we see to be the cause in the sciences, that by reason of which all intellect and all 
nature operates, on that cause which we say is one of the principles the Forms do not touch in 
any way. But mathematics has been turned into philosophy by present-day thinkers (566), 
although they say that mathematics must be treated for the sake of other things. 

134. Further, one might suppose that the underlying substance [which they consider] as 
matter is too mathematical, and that it is rather a predicate and difference of substance and 
matter, like the great and small; just as the philosophers of nature speak of the rare and dense 
(56), which they say are the primary differences of the underlying subject; for " these are a 
kind of excess and defect. 

135. And with regard to motion, if these entities [the great and small] are motion, evidently 
the Forms are moved; but if they are not, from what does motion come? For [if it has no 
cause] , the whole study of nature is destroyed. 

136. And what seems easy to show is that all things are not one; for from their position all 
things do not become one. But if someone should assert that all things are some one thing, not 
even this is true unless one grants that the universal is a class; and in certain other cases this is 
impossible. 

137. For they do not have any theory about the lengths, widths, and solids which come after 
the numbers: either as to how they now exist or will exist, or what importance they have. For 
it is impossible that they should be Forms (since they are not numbers), or intermediate things 
(for those are the objects of mathematics), or corruptible things; but, on the contrary, it seems 
that they form a fourth class. 

138. And, in general, to look for the elements of existing things without distinguishing the 
different senses in which things are said to be, makes it impossible to discover them. And 
[their view is unsatisfactory] in another way, i.e., in the way in which they seek for the 
elements of which things are composed. For it is impossible to understand of what things 
action or passion or straightness is composed. But if this is possible only in the case of 
substances, then to look for the elements of all existing things, or to think that we have found 
them, is a mistake. 

139. But how will one acquire knowledge of the elements of all things? For it is clearly 
impossible to have prior knowledge of anything. For just as one acquiring knowledge of 
geometry must have a prior knowledge of other things, but not of the things which this 
science [investigates], and which he is to learn, so it is in the case of the other sciences. 
Hence, if there is a science of all things (and there must be a science of these), as some say, 
the one learning this science does not have any prior knowledge of it. But all learning 
proceeds from things previously known, either all or some of them, whether the learning be 
by demonstration or by definitions. For [the parts] of which definitions are composed must 
already be known beforehand and be evident. The same thing is true in the case of things 
discovered by induction. 


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140. But if this science were connatural, it is a wonder how we could be unconscious of 
having the most important of the sciences. 

141. Again, how is anyone to know the elements of which things are composed, and how is 
this to be made evident? For this also presents a difficulty; because one might argue in the 
same way as one does about certain syllables. For some say that sma is made up of s, m and a, 
whereas others say that it is a totally different sound and not any of those which are known to 
us. 

142. Again, how could one know the things of which a sense is cognizant without having that 
sense? Yet this will be necessary if they [i.e., sensible things] are the elements of which all 
things are composed, just as spoken words are composed of their proper elements. 

Chapter 10 

143. From the foregoing, then, it is evident that all [the early philosophers] seem to seek the 
causes mentioned in the Physics, and that we cannot state any other in addition to these. But 
they understood these obscurely; and while in one sense all causes have been mentioned 
before, in another sense they have not been mentioned at all. Indeed, the earliest philosophy 
seems to speak in a faltering way about all subjects inasmuch as it was new as regards 
principles and the first of its kind. For even Empedocles says that ratios are present in bone, 
and that this is the quiddity or substance of a thing. But [if this is true], there must likewise be 
a ratio of flesh and of every other thing or of nothing. For it is because of this that flesh and 
bone and every other thing exists, and not because of their matter, which he says is fire, earth, 
air and water. But if someone else had said this, he would have been forced to agree to the 
same thing. But he has not said this. Such things as these, then, have been explained before. 
So let us return again to whatever problems one might raise about the same subject; for 
perhaps in the light of these we shall be able to make some investigation into subsequent 
problems. 

COMMENTARY 

259. Here Aristotle destroys Plato's opinion about the principles of things. First, he destroys 
Plato's opinion about principles of being; and second (268), his opinion about principles of 
knowledge ("But how will one"). 

In regard to the first part he gives six arguments. The first is based on the fact that Plato 
neglected to deal with the classes of causes. Thus he says that, "in general, wisdom," or 
philosophy, has as its aim to investigate the causes "of apparent things," i.e., things apparent 
to the senses. For men began to philosophize because they sought for the causes of things, as 
was stated in the prologue (53). But the Platonists, among whom he includes himself, 
neglected the principles of things, because they said nothing about the efficient cause, which 
is the source of change. And by positing the Ideas they thought they had given the formal 
cause of things. But while they thought that they were speaking of the substance of these 
things, i.e., sensible ones, they posited the existence of certain other separate substances 
which differ from these. However, the way in which they assigned these separate substances 
as the substances of sensible things "is empty talk," i.e., it proves nothing and is not true. For 
they said that the Forms are the substances of sensible things inasmuch as they are 
participated in by sensible things. But what they said about participation is meaningless, as is 
clear from what was said above (225). Furthermore, the Forms which they posited have no 
connection with the final cause, although we see that this is a cause in certain sciences which 


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demonstrate by means of the final cause, and that it is by reason of this cause that every 
intellectual agent and every natural one operates, as has been shown in the Physics, Book II. 
And just as they do not touch on that cause which is called an end [or goal], when they 
postulate the existence of the Forms (169), neither do they treat of that cause which is called 
the source of motion, namely, the efficient cause, which is the opposite, so to speak, of the 
final cause. But the Platonists by omitting causes of this kind (since they did omit a 
starting-point and end of motion), have dealt with natural things as if they were objects of 
mathematics, which lack motion. Hence they said that the objects of mathematics should be 
studied not only for themselves but for the sake of other things, i.e., natural bodies; inasmuch 
as they attributed the properties of the objects of mathematics to sensible bodies. 

260. Further, one might (134). 

Here he gives the second argument, which runs thus: that which is posited as the matter of a 
thing is the substance of a thing, and is predicable of a thing to a greater degree than 
something which exists apart from it. But a Form exists apart from sensible things. Therefore, 
according to the opinion of the Platonists, one might suppose that the underlying substance as 
matter is the substance of the objects of mathematics rather than a separate Form. 
Furthermore, he admits that it is predicated of a sensible thing rather than the above Form. 
For the Platonists held that the great and small is a difference of substance or matter; for they 
referred these two principles to matter, just as the philosophers of nature (115) held that rarity 
and density are the primary differences of the "underlying subject," or matter, by which 
matter is changed, and spoke of them in a sense as the great and small. This is clear from the 
fact that rarity and density are a kind of excess and defect. For the dense is what contains a 
great deal of matter under the same dimensions, and the rare is what contains very little 
matter. Yet the Platonists said that the Forms are the substance of sensible things rather than 
the objects of mathematics, and that they are predicable of them to a greater degree. 

261. And with regard (135). 

Here he gives the third argument, which runs thus: if those attributes which exist in sensible 
things are caused by separate Forms, it is necessary to say either that there is an Idea of 
"motion" among the Forms or there is not. If there is a Form or Idea of motion among the 
Forms, and there cannot be motion without something that is moved, it also follows that the 
Forms must be moved. But this is opposed to the Platonists' opinion, for they claimed that the 
Forms are immobile. On the other hand, if there is no Idea of motion, and these attributes 
which exist in sensible things are caused by the Ideas, it will be impossible to assign a cause 
for the motion which occurs in sensible things; and thus the entire investigation of natural 
philosophy, which studies mobile things, will be destroyed. 

262. And what seems easy (136). 

Then he gives the fourth argument, which runs thus: if unity were the substance of all things, 
as the Platonists assumed, it would be necessary to say that all things are one, just as the 
philosophers of nature also did in claiming that the substance of all things is water, and so on 
for the other elements. But it is easy to show that all things are not one. Hence the position 
that unity is the substance of all things is not held in high repute. 

263. But let us assume that someone might say that it does not follow, from Plato's position, 
that all things are one in an unqualified sense but in a qualified sense, just as we say that some 
things are one generically or specifically. And if someone wished to say that all things are one 


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in this way, even this could be held only if what I call the one were a genus or universal 
predicate of all things. For then we could say that all things are one specifically, just as we 
say that both a man and an ass are animal substantially. But in certain cases it seems 
impossible that there should be one class of all things, because the difference dividing this 
class would necessarily not be one, as will be said in Book III (432). Therefore, in no way can 
it be held that the substance of all things is one. 

264. For they do not have (137). 

Here he gives the fifth argument, which runs thus: Plato placed lengths, widths and solids 
after numbers as the substances of sensible things, i.e., that of which they are composed. But 
according to Plato's position there seems to be no reason why they should be held to exist 
either now or in the future. Nor does this notion seem to have any efficacy to establish them 
as the causes of sensible things. For things which exist "now" must mean immobile things 
(because these always exist in the same way), whereas things which "will exist" must mean 
those which are capable of generation and corruption, which acquire being after non-being. 
This becomes clear thus: Plato posited three classes of things — sensible things, the Forms and 
the objects of mathematics, which are an intermediate class. But such lines and surfaces as 
those of which sensible bodies are composed cannot be Forms; for the Forms are essentially 
numbers, whereas such things [i.e., the lines and surfaces composing bodies] come after 
numbers. Nor can such lines and surfaces be said to be an intermediate class between the 
Forms and sensible things; for the things in this intermediate class are the objects of 
mathematics, and exist apart from sensible things; but this cannot be said of the lines and 
surfaces of which sensible bodies are composed. Nor again can such lines and surfaces be 
sensible things; for the latter are corruptible, whereas these lines and surfaces are 
incorruptible, as will be proved below in Book III (466). Therefore these things are either 
nothing at all or they constitute a fourth class of things, which Plato omitted. 

265. And, in general (138). 

Here he gives the sixth argument, which runs thus: it is impossible to discover the principles 
of anything that is spoken of in many senses, unless these many senses are distinguished. 
Now those things which agree in name only and differ in their intelligible structure cannot 
have common principles; otherwise they would have the same intelligible structure, since the 
intelligible structure of a thing is derived from its own principles. But it is impossible to 
assign distinct principles for those things which have only the name in common, unless it be 
those whose principles must be indicated to differ from each other. Therefore, since being is 
predicated both of substance and the other genera in different senses and not in the same 
sense, Plato assigned inadequate principles for things by failing to distinguish beings from 
each other. 

266. But since someone could assign principles to things which differ in their intelligible 
structure and have a common name, by adjusting proper principles to each without 
distinguishing the many senses of the common name, and since the Platonists have not done 
this, then "in another way," i.e., by another argument, they assigned inadequate principles to 
things when they looked for the elements of which things are made, i.e., in the way in which 
they sought for them, inasmuch as they did not assign principles which are sufficient for all 
things. For from their statements it is impossible to understand the principles of which either 
action and passion, curvature and straightness, or other such accidents, are composed. For 
they only indicated the principles of substances and neglected accidents. 


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267. But if in defense of Plato someone wished to say that it is possible for the elements of all 
things to have been acquired or discovered at the moment when the principles of substances 
alone happen to have been acquired or discovered, this opinion would not be true. For even if 
the principles of substances are also in a sense the principles of accidents, nevertheless 
accidents have their own principles. Nor are the principles of all genera the same in all 
respects, as will be shown below in Book XI (2173) and Book XII (2455) of this work. 

268. But how will one (139). 

Here he argues dialectically against Plato's position that the Ideas are the principles of our 
scientific knowledge. He gives four arguments, of which the first is this: if our scientific 
knowledge is caused by the Ideas themselves, it is impossible for us to acquire knowledge of 
the principles of things. But it is evident that we do acquire knowledge. Therefore our 
knowledge is not caused by the Ideas themselves. That it would be impossible to acquire 
knowledge of anything, he proves thus: no one has any prior knowledge of that object of 
which he ought to acquire knowledge; for example, even though in the case of geometry one 
has prior knowledge of other things which are necessary for demonstration, nevertheless the 
objects of which he ought to acquire knowledge he must not know beforehand. The same 
thing is also true in the case of the other sciences. But if the Ideas are the cause of our 
knowledge, men must have knowledge of all things, because the Ideas are the intelligible 
structures of all knowable things. Therefore we cannot acquire knowledge of anything) unless 
one might be said to acquire knowledge of something, which he already knew, if it is held, 
then, that someone acquires knowledge, he must not have any prior knowledge of the thing 
which he comes to know, but only of certain other things through which he becomes 
instructed; i.e., one acquires knowledge through things previously known, [either] "all," i.e., 
universals, "or some of them," i.e., singular things. One learns through universals in the case 
of those things which are discovered by demonstration and definition, for in the case of 
demonstrations and definitions the things of which definitions or universals are composed 
must be known first. And in the case of things which are discovered by induction singular 
things must be known first. 

269. But if this, science (140). 

Here he gives the second argument, which runs thus: if the Ideas are the cause of our 
knowledge, it must be connatural to us; for men grasp sensible things through this proper 
nature, because sensible things participate in Ideas according to the Platonists. But the most 
important knowledge or science is one that is connatural to us and which we cannot forget, as 
is evident of our knowledge of the first principles of demonstration, of which no one is 
ignorant. Hence there is no way in which we can forget the knowledge of all things caused in 
us by the Ideas. But this is contrary to the Platonists' opinion, who said that the soul as a 
result of its union with the body forgets the knowledge which it has of all things by nature, 
and that by teaching a man acquires knowledge of something that he previously knew, as 
though the process of acquiring knowledge were merely one of remembering. 

270. Again, how is anyone (141). 

Here he gives the third argument, which runs thus: in order to know things a man must 
acquire knowledge not only of the forms of things but also of the material principles of which 
they are composed. This is evident from the fact that occasionally questions arise regarding 
these; for example, with regard to this syllable sma, some raise the question whether it is 
composed of the three letters s, m and a, or whether it is one letter which is distinct from these 


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and has its own sound. But only the formal principles of things can be known through the 
Ideas, because the Ideas are the forms of things. Hence the Ideas are not a sufficient cause of 
our knowledge of things when material principles remain unknown. 

271. Again, how could (142). 

Here he gives the fourth argument, which runs thus: in order to know reality we must know 
sensible things, because sensible things are the apparent material element of which all things 
are composed, just as complex sounds (such as syllables and words) are composed of their 
proper elements. If, then, knowledge is caused in us by the Ideas, our knowledge of sensible 
things must be caused by the Ideas. But the knowledge which is caused in us by the Ideas is 
grasped without the senses, because we have no connection with the Ideas through the senses. 
Therefore in the act of perception it follows that anyone who does not have a sense can 
apprehend the object of that sense. This is clearly false; for a man born blind cannot have any 
knowledge of colors. 

272. From the foregoing (143). 

Here he summarizes the statements made by the ancient philosophers. He says that from what 
has been said above it is evident that the ancient philosophers attempted to investigate the 
cause which he [Aristotle] dealt with in the Physics, and that in their statements we find no 
cause in addition to those established in that work. However, these men discussed these 
causes obscurely; and while in a sense they have mentioned all of these causes, in another 
sense they have not mentioned any of them. For just as young children at first speak 
imperfectly and in a stammering way, in a similar fashion this philosophy, since it was new, 
seems to speak imperfectly and in a stammering way about the principles of all things. This is 
borne out by the fact that Empedocles was the first to say that bones have a certain ratio, or 
proportional mixture [of the elements], and that this is a thing's quiddity or substance. But the 
same thing must also be true of flesh and of every other single thing or of none of them, for 
all of these things are mixtures of the elements. And for this reason it is evident that flesh and 
bone and all things of this kind are not what they are because of their matter, which he 
identified with the four elements, but because of this principle-their form. However, 
Empedocles, compelled as it were by the need for truth, would have maintained this view if it 
had been expressed more clearly by someone else, but he did not express it clearly. And just 
as the ancient philosophers have not clearly expressed the nature of form, neither have they 
clearly expressed the nature of matter, as was said above about Anaxagoras (90). Nor have 
they clearly expressed the nature of any other principles. Therefore, concerning such thing, as 
have been stated imperfectly, we have spoken of this before (190). And with regard to these 
matters we will restate again in Book III (423) whatever difficulties can be raised on both 
sides of the question. For perhaps from such difficulties we will discover some useful 
information for dealing with the problems which must be examined and solved later on 
throughout this whole science. 


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METAPHYSICS 
BOOK II 


THE SEARCH FOR TRUTH AND CAUSES 


CONTENTS 


LESSON 2: 


LESSON 1: 


The Acquisition of Truth: Its Ease and Its Difficulty 

The Supreme Science of Truth, and Knowledge of Ultimate 
Causes 


LESSON 3: 


The Existence of a First Efficient Cause and of a First Material 
Cause 


LESSON 4: 


The Existence of a First in Final and Formal Causes 


LESSON 5: The Method to Be Followed in the Search for Truth 


LESSON 1 

The Acquisition of Truth: Its Ease and Its Difficulty 
ARISTOTLE'S TEXT Chapter 1: 993a 30-993b 19 

144. Theoretical, i.e., speculative, knowledge of truth is in one sense difficult and in another, 
easy. 

145. An indication of this is found in the fact that, while no one can attain an adequate 
knowledge of it, all men together do not fail, because each one is able to say something true 
about nature. 

146. And while each one individually contributes nothing or very little to the truth, still as a 
result of the combined efforts of all a great amount of truth becomes known. 

147. Therefore, if the situation in the case of truth seems to be like the one which we speak of 
in the proverb "Who will miss a door?" then in this respect it will be easy to know the truth. 

148. But the fact that we cannot simultaneously grasp a whole and its parts shows the 
difficulty involved." 

149. However, since the difficulty is twofold, perhaps its cause is not in things but in us; for 
just as the eyes of owls are to the light of day, so is our soul's intellective power to those 
things which are by nature the most evident of all. 

150. Now it is only right that we should be grateful not merely to those with whose views we 
agree but also to those who until now have spoken in a superficial way; for they too have 
made some contribution because they have made use of the habit which we now exercise. 
Thus if there had been no Timotheus, we would not have a great part of our music; and if 
there had been no Phrynis, there would have been no Timotheus. The same is true of those 


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who have made statements about the truth; for we have accepted certain opinions from some 
of them, and others have been the cause of them attaining their knowledge as they have been 
the cause of us attaining ours. 

COMMENTARY 

273. Having criticized the ancient philosophers' opinions about the first principles of things, 
with which first philosophy is chiefly concerned, the Philosopher now begins to establish 
what is true. 

First philosophy considers truth in a different way than the particular sciences do. Each of the 
particular sciences considers a particular truth out a definite class of beings; e.g., geometry 
deals with the continuous quantities of bodies, and arithmetic with numbers; whereas first 
philosophy considers what is universally true of things. Therefore, it pertains to this science to 
consider in what respects man is capable of knowing the truth. 

274. First, he states what he intends to prove. He says that "theoretical knowledge," i.e., the 
contemplative or speculative understanding of truth, is in one sense easy and in another, 
difficult. 

275. An indication of this (145). 

Second, he explains what he intends to prove: first, in what sense it is easy to know the truth; 
and second (278), in what sense it is difficult ("But the fact"). He shows in what sense it is 
easy to know the truth, by giving three indications: 

The first is this: while no man can attain a complete knowledge of the truth, still no man is so 
completely devoid of truth that he knows nothing about it. This is shown by the fact that 
anyone can make a statement about the truth and the nature of things, which is a sign of 
intellectual reflection. 

276. And while each one individually (146). 

Here he gives the second indication. He says that, while the amount of truth that one man can 
discover or contribute to the knowledge of truth by his own study and talents is small 
compared with a complete knowledge of truth, nevertheless what is known as a result of "the 
combined efforts" of all, i.e., what is discovered and collected into one whole, becomes quite 
extensive. This can be seen in the case of the particular arts, which have developed in a 
marvelous manner as a result of the studies and talents of different men. 

277. Therefore, if the situation (147). 

Third, he shows that the same thing is true by citing a common proverb. He concludes from 
the foregoing that since anyone can attain some knowledge of the truth, even though it be 
little, the situation in the case of knowledge is like the one that we speak of in the proverb 
"Who will miss a door?" i.e., the outer door of a house. For it is difficult to know what the 
interior of a house is like, and a man is easily deceived in such matters; but just as no one is 
mistaken about the entrance of a house, which is evident to all and is the first thing that we 
perceive, so too this is the case with regard to the knowledge of truth; for those truths through 
which we enter into a knowledge of others are known to all, and no man is mistaken about 
them. Those first principles which are naturally apprehended are truths of this sort, e.g., "It is 


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impossible both to affirm and deny something at the same time," and "Every whole is greater 
than each of its parts," and so on. On the other hand, there are many ways in which error may 
arise with respect to the conclusions into which we enter through such principles as through 
an outer door. Therefore, it is easy to know the truth if we consider that small amount of it 
which is comprised of self-evident principles, through which we enter into other truths, 
because this much is evident to all. 

278. But the fact that we cannot (148). 

Here he explains in what sense it is difficult to know the truth. He says that our inability to 
grasp the whole truth and a part of it shows the difficulty involved in the search for truth. In 
support of this we must consider his statement that the truth through which we gain admission 
to other truths is known to all. Now there are two ways in which we attain knowledge of the 
truth. 

The first is the method of analysis, by which we go from what is complex to what is simple or 
from a whole to a part, as it is said in Book I of the Physics that the first objects of our 
knowledge are confused wholes. Now our knowledge of the truth is perfected by this method 
when we attain a distinct knowledge of the particular parts of a whole. 

The other method is that of synthesis, by which we go from what is simple to what is 
complex; and we attain knowledge of truth by this method when we succeed in knowing a 
whole. Thus the fact that man is unable to know perfectly in things a whole and a part shows 
the difficulty involved in knowing the truth by both of these methods. 

279. However, since the difficulty is twofold (149). 

He gives the reason for this difficulty. Here too it must be noted that, in all cases in which 
there is a certain relationship between two things, an effect can fail to occur in two ways, i.e., 
because of either one of the things involved. For example, if wood does not burn, this may 
happen either because the fire is not strong enough or because the wood is not combustible 
enough. And in a similar way the eye may be prevented from seeing a visible object either 
because the eye is weak or because the visible object is in the dark. Therefore, in like manner, 
it may be difficult to know the truth about things either (1) because things themselves are 
imperfect in some way or (2) because of some weakness on the part of our intellect. 

280. (1) Now it is evident that we experience difficulty in knowing the truth about some 
things because of the things themselves; for since each thing is know able insofar as it is an 
actual being, as will be stated below in Book IX (1894) of this work, then those things which 
are deficient and imperfect in being are less knowable by their very nature; e.g., matter, 
motion, and time are less knowable because of the imperfect being which they have, as 
Boethius says in his book The Two Natures. 

28 1 . Now there were some philosophers who claimed that the difficulty experienced in 
knowing the truth is wholly attributable to things themselves, because they maintained that 
nothing is fixed and stable in nature but that everything is in a state of continual change, as 
will be stated in Book IV (683) of this work. But the Philosopher denies this, saying that even 
though the difficulty experienced in knowing the truth can perhaps be twofold because of 
different things, i.e., our intellect and things themselves, still the principal source of the 
difficulty is not things but our intellect. 


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282. He proves this in the following way. If this difficulty were attributable principally to 
things, it would follow it we would know best those things which are most knowable by 
nature. But those things which are most knowable by nature are those which are most actual, 
i.e., immaterial and unchangeable things, yet we know these least of all. 

Obviously, then, the difficulty experienced in knowing the truth is due principally to some 
weakness on the part of our intellect. From this it follows that our soul' s intellectual power is 
related to those immaterial beings, which are by nature the most knowable of all, as the eyes 
of owls are to the light of day, which they cannot see because their power of vision is weak, 
although they do see dimly lighted things. 

283. But it is evident that this simile is not adequate; for since a sense is a power of a bodily 
organ, it is made inoperative as a result of its sensible object being too intense. But the 
intellect is not a power of a bodily organ and is not made inoperative as a result of its 
intelligible object being too intelligible. Therefore, after understanding objects that are highly 
intelligible our ability to understand less intelligible objects is not decreased but increased, as 
is stated in Book III of The Soul. 

284. Therefore it must be said that a sense is prevented from perceiving some sensible object 
for two reasons: first, (1) because a sensory organ is rendered inoperative as a result of its 
sensible object being too intense (this does not occur in the case of the intellect); second, (2) 
because of some deficiency in the ability of a sensory power to perceive its object; for the 
powers of the soul in all animals do not have the same efficacy. Thus, just as it is proper to 
man by nature to have the weakest sense of smell, in a similar way it is proper to an owl to 
have the weakest power of vision, because it is incapable of perceiving the light of day. 

285. Therefore, since the human soul occupies the lowest place in the order of intellective 
substances, it has the least intellective power. As a matter of fact, just as it is by nature the 
actuality of a body, although its intellective power is not the act of a bodily organ, in a similar 
way it has a natural capacity to know the truth about corporeal and sensible things. These are 
less knowable by nature because of their materiality, although they can be known by 
abstracting sensible forms from phantasms. And since this process of knowing truth befits the 
nature of the human soul insofar as it is the form of this kind of body (and whatever is natural 
always remains so), it is possible for the human soul, which is united to this kind of body, to 
know the truth about things only insofar as it can be elevated to the level of the things which 
it understands by abstracting from phantasms. However, by this process it cannot be elevated 
to the level of knowing the quiddities of immaterial substances because these are not on the 
same level as sensible substances. Therefore it is impossible for the human soul, which is 
united to this kind of body, to apprehend separate substances by knowing their quiddities. 

286. For this reason the statement which Averroes makes at this point in his Commentary is 
evidently false, i.e., that the Philosopher does not prove here that it is just as impossible for us 
to understand abstract substances as it is for a bat to see the sun. The argument that he gives is 
wholly ridiculous; for he adds that, if this were the case, nature would have acted in vain 
because it would have made something that is naturally knowable in itself to be incapable of 
being known by anything else. It would be the same as if it had made the sun incapable of 
being seen. 

This argument is not satisfactory for two reasons. First, the end of separate substances does 
not consist in being understood by our intellect, but rather the converse. Therefore, if separate 
substances are not known by us, it does not follow that they exist in vain; for only that exists 


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in vain which fails to attain the end for which it exists. Second, even though the quiddities of 
separate substances are not understood by us, they are understood by other intellects. The 
same is true of the sun; for even though it is not seen by the eye of the owl, it is seen by the 
eye of the eagle. 

287. Now it is only right (150). 

He shows how men assist each other to know the truth; for one man assists another to 
consider the truth in two ways — directly and indirectly. 

One is assisted directly by those who have discovered the truth; because, as has been pointed 
out, when each of our predecessors has discovered something about the truth, which is 
gathered together into one whole, he also introduces his followers to a more extensive 
knowledge of truth. 

One is assisted indirectly insofar as those who have preceded us and who were wrong about 
the truth have bequeathed to their successors the occasion for exercising their mental powers, 
so that by diligent discussion the truth might be seen more clearly. 

288. Now it is only fitting that we should be grateful to those who have helped us attain so 
great a good as knowledge of the truth. Therefore he says that "It is only right that we should 
be grateful," not merely to those whom we think have found the truth and with whose views 
we agree by following them, but also to those who, in the search for truth, have made only 
superficial statements, even though we do not follow their views; for these men too have 
given us something because they have shown us instances of actual attempts to discover the 
truth. By way of an example he mentions the founders of music; for if there "had been no 
Timotheus," who discovered a great part of the art of music, we would not have many of the 
facts that we know about melodies. But if Timotheus had not been preceded by a wise man 
named "Phrynis," he would not have been as well off in the subject of music. The same thing 
must be said of those philosophers who made statements of universal scope about the truth of 
things; for we accept from certain of our predecessors whatever views about the truth of 
things we think are true and disregard the rest. Again, those from whom we accept certain 
views had predecessors from whom they in turn accepted certain views and who were the 
source of their information. 


LESSON 2 

The Supreme Science of Truth, and Knowledge of Ultimate Causes 
ARISTOTLE'S TEXT Chapters 1 & 2: 993b 19-994b 11 

151. It is only right to call philosophy the science of truth. For the end of theoretical 
knowledge is truth, whereas that of practical knowledge is action; for even when practical 
men investigate the way in which something exists, they do not consider it in itself but in 
relation to some particular thing and to the present moment. But we know a truth only by 
knowing its cause. Now anything which is the basis of a univocal predication about other 
things has that attribute in the highest degree. Thus fire is hottest and is actually the cause of 
heat in other things. Therefore that is also true in the highest degree which is the cause of all 


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subsequent things being true. For this reason the principles of things that always exist must 
be. true in the highest degree, because they are not sometimes true and sometimes not true. 
Nor is there any cause of their being, but they are the cause of the being of other things. 
Therefore insofar as each thing has being, to that extent it is true. 

Chapter 2 

152. Further, it is evident that there is a [first] principle, and that the causes of existing things 
are not infinite either in series or in species. For it is impossible that one thing should come 
from something else as from matter in an infinite regress, for example, flesh from earth, earth 
from air, air from fire, and so on to infinity. Nor can the causes from which motion originates 
proceed to infinity, as though man were moved by the air, the air by the sun, the sun by strife, 
and so on to infinity. Again, neither can there be an infinite regress in the case of the reason 
for which something is done, as though walking were for the sake of health, health for the 
sake of happiness, and happiness for the sake of something else, so that one thing is always 
being done for the sake of something else. The same is true in the case of the quiddity. 

COMMENTARY 

289. Having shown how man is disposed for the study of truth, the Philosopher now shows 
that the knowledge of truth belongs pre-eminently to first philosophy. Regarding this he does 
two things... First (290), he shows that knowledge of the truth belongs pre-eminently to first 
philosophy. Second (290), that it belongs in the highest degree to this science ("But we know 
a truth"). 

He proves these two propositions from two things established above in the prologue of this 
book, i.e., that wisdom is not a practical but a speculative science (53), and that it knows first 
causes (48). 

290. He argues from the first of these to the first conclusion in this way. Theoretical, i.e., 
speculative, knowledge differs from practical knowledge by its end; for the end of speculative 
knowledge is truth, because it has knowledge of the truth as its objective. But the end of 
practical knowledge is action, because, even though "practical men," i.e., men of action, 
attempt to understand the truth as it belongs to certain things, they do not seek this as an 
ultimate end; for they do not consider the cause of truth in and for itself as an end but in 
relation to action, either by applying it to some definite individual, or to some definite time. 
Therefore, if we add to the above the fact that wisdom or first philosophy is not practical but 
speculative, it follows that first philosophy is most fittingly called the science of truth. 

291. But since there are many speculative sciences, which consider the truth, such as 
geometry and arithmetic, therefore it was necessary to show that first philosophy considers 
truth in the highest degree inasmuch as it has been shown above that it considers first causes 
(48). Hence he argues as follows. We have knowledge of truth only when we know a cause. 
This is apparent from the fact that the true things about which we have some knowledge have 
causes which are also true, because we cannot know what is true by knowing what is false, 
but only by knowing what is true. This is also the reason why demonstration, which causes 
science, begins with what is true, as is stated in Book I of the Posterior Analytics . 

292. Then he adds the following universal proposition. When a univocal predicate is applied 
to several things, in each case that which constitutes the reason for the predication about other 
things has that attribute in the fullest sense. Thus fire is the cause of heat in compounds. 


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Therefore, since heat is predicated univocally both of fire and of compound bodies, it follows 
that fire is hottest. 

293. Now he says "univocal" because sometimes it happens that an effect does not become 
like its cause, so as to have the same specific nature, because of the excellence of that cause; 
for example, the sun is the cause of heat in these lower bodies, but the form which these lower 
bodies receive cannot be of the same specific nature as that possessed by the sun or any of the 
celestial bodies, since they do not have a common matter. This is why we do not say that the 
sun is hottest, as we say fire is, but that it is something superior to the hottest. 

294. Now the term truth is not proper to one class of beings only, but is applied universally to 
all beings. Therefore, since the cause of truth is one having the same name, and intelligible 
structure as its effect, it follows that whatever causes subsequent things to be true is itself 
most true. 

295. From this he again concludes that the principles of things which always exist, i.e., the 
celestial bodies, must be most true. He does this for two reasons. First, they are not 
"sometimes true and sometimes not true," and therefore surpass the truth of things subject to 
generation and corruption, which sometimes exist and sometimes do not. Second, these 
principles have no cause but are the cause of the being of other things. And for this reason 
they surpass the celestial bodies in truth and in being; and even though the latter are 
incorruptible, they have a cause not only of their motion, as some men thought, but also of 
their being, as the Philosopher clearly states in this place. 

296. Now this is necessary, because everything that is composite in nature and participates in 
being must ultimately have as its causes those things which have existence by their very 
essence. But all corporeal things are actual beings insofar as they participate in certain forms. 
Therefore a separate substance which is a form by its very essence must be the principle of 
corporeal substance. 

297. If we add to this conclusion the fact that first philosophy considers first causes, it then 
follows, as was said above (291), that first philosophy considers those things which are most 
true. Consequently this science is pre-eminently the science of truth. 

298. From these conclusions he draws a corollary: since those things which cause the being of 
other things are true in the highest degree, it follows that each thing is true insofar as it is a 
being; for things which do not always have being in the same way do not always have truth in 
the same way, and those which have a cause of their being also have a cause of their truth. 
The reason for this is that a thing's being is the cause of any true judgment which the mind 
makes about a thing; for truth and falsity are not in things but in the mind, as will be said in 
Book VI (1230) of this work. 

299. He rejects a position that would render the above proof untenable; for this proof 
proceeded on the supposition that first philosophy considers first causes. But if there were an 
infinite regress in causes, this proof would be destroyed, for then there would be no first 
cause. So his aim here is to refute this position. Concerning this he does two things. First 
(152), he points out what he intends to prove. Second (300, he proceeds to do so. 

He says, first, that from what has been said it can clearly be shown that there is some [first] 
principle of the being and truth of things. He states that the causes of existing things are not 
infinite in number because we cannot proceed to infinity in a series of causes belonging to 


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one and the same class, e.g., the class of, efficient causes. Nor again are causes infinite in 
species, as though the classes of causes were infinite in number. 

300. Then he explains his statement about an infinite number of causes in a series. He does 
this, first, in regard to the class of material causes. For it is impossible to have an infinite 
series in the sense that one thing always comes from something else as its matter, e.g., that 
flesh comes from earth, earth from air, and air from fire, and that this does not terminate in 
some first entity but goes on to infinity. 

Second, he gives an example of this in the class of efficient cause. He says that it is 
impossible to have an infinite series in the class of cause which we define as the source of 
motion; e.g., when we say that a man is moved to put aside his clothing because the air 
becomes warm, the air having been heated in turn by the sun, the sun having been moved by 
something else, and so on to infinity. 

Third, he gives an example of this in the class of final causes. He says that it is also 
impossible to proceed to infinity in the case of "the reason for which" something is done, i.e., 
the final cause; for example, if we were to say that a journey or a walk is undertaken for the 
sake of health, health for the sake of happiness, happiness for the sake of something else, and 
so on to infinity. 

Finally, he mentions the formal cause. He says that it is also impossible to proceed to infinity 
in the case of the "quiddity," i.e., the formal cause, which the definition signifies. However, 
he omits examples because these are evident, and because it was shown in Book I of the 
Posterior Analytics that it is impossible to proceed to infinity in the matter of predication, as 
though animal were predicated quidditatively of man, living of animal, and so on to infinity. 


LESSON 3 

The Existence of a First Efficient Cause and of a First Material Cause 
ARISTOTLE'S TEXT Chapter 2: 994a ll-994b 9 

153. For intermediate things in a series limited by some first and last thing must have as their 
cause the first member of the series, which they follow; because if we had to say which one of 
these three is the cause of the others, we would say that it is the first. What is last is not the 
cause, since what is last is not a cause of anything. Neither is the intermediate the cause, 
because it is the cause of only one; for it makes no difference whether one or several 
intermediates exist, or an infinite or finite number. Indeed, in series that are infinite in this 
way or in the infinite in general, all parts are intermediates to the same degree right down to 
the present one. Therefore, if there is nothing first in the whole series, nothing in the series is 

a cause. 

154. Neither is it possible to proceed to infinity in a downward direction, where there is a 
starting-point in an upward direction, so that water comes from fire, earth from water, and 
some other class of things always being generated in this way. 


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155. Now there are two ways in which one thing comes from (ex) another. I do not mean from 
in the sense of after, as the Olympian games are said to come from the Isthmian, but either in 
the way in which a man comes from a boy as a result of a boy changing, or in the way in 
which air comes from water. 

156. We say, then, that a man comes from a boy in the sense that what has come into being 
comes from what is coming into being, or in the sense that what has been completed comes 
from what is being completed. For generation is always midway between being and 
non-being, and thus whatever is coming into being is midway between what is and what is 
not. Now a learner is one who is becoming learned, and this is the meaning of the statement 
that the man of science comes from the learner. But water comes from air in the sense that it 
comes into being when the latter ceases to be. 

157. This is why changes of the former kind are not reversible, and thus a boy does not come 
from a man. The reason is that the thing which comes into being does not come from 
generation but exists after generation. This is the way in which the day comes from the dawn, 
i.e., in the sense that it exists after the dawn; and this is why the dawn cannot come from the 
day. On the other hand, changes of the latter sort are reversible. 

158. Now in neither way is it possible to proceed to infinity; for existing intermediaries must 
have some end, and one thing may be changed into the other because the corruption of one is 
the generation of the other. 

159. At the same time it is impossible that an eternal first cause should be corrupted; for since 
generation is not infinite in an upward direction, then a first principle by whose corruption 
something else is produced could not be eternal. 

COMMENTARY 

301. Having assumed above that the causes of beings are not infinite in number, the 
Philosopher now proves this. First (153:C 300, he proves that there are not an infinite number 
of causes in a series; and second (170:C 330), that the classes of causes are not infinite in 
number ("Again, if the classes of causes"). 

In regard to the first he does four things. First, he proves his assumption in the case of 
efficient or moving causes; second (154:C 305), in the case of material causes ("Neither is it 
possible"); third (160:C 316), in the case of final causes ("Again, that for the sake of which"); 
and fourth (164:C 320), in the case of formal causes ("Nor can the quiddity"). 

In regard to the first he proceeds as follows. First, he lays down this premise: in the case of all 
those things which lie between two extremes, one of which is last and the other first, the first 
is necessarily the cause of those which come after it, namely, what is intermediate and what is 
last. 

302. Then he proves this premise by a process of elimination. For if we had to say which of 
the three, i.e., the first, the intermediate, or the last, is the cause of the others, we would have 
to say that the first is the cause. We could not say that what is last is the cause of all the 
others, because it is not a cause of anything; for in other respects what is last is not a cause, 
since an effect follows a cause. Nor could we say that the intermediate is the cause of all the 
others, because it is the cause of only one of them, namely, what is last. 


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303. And lest someone should think that an intermediate is followed by only one thing, i.e., 
what is last (for this occurs only when there is a single thing between two extremes), in order 
to exclude this interpretation he adds that it makes no difference to the premise given above 
whether there is only one intermediate or several, because all intermediates are taken together 
as one insofar as they have in common the character of an intermediate. Nor again does it 
make any difference whether there are a finite or infinite number of intermediates, because so 
long as they have the nature of an intermediate they cannot be the first cause of motion. 
Further, since there must be a first cause of motion prior to every secondary cause of motion, 
then there must be a first cause prior to every intermediate cause, which is not an intermediate 
in any sense, as though it had a cause prior to itself. But if we were to hold that there is an 
infinite series of moving causes in the above way, then all causes would be intermediate ones. 
Thus we would have to say without qualification that all parts of any infinite thing, whether 
of a series of causes or of continuous quantities, are intermediate ones; for if there were a part 
that was not an intermediate one, it would have to be either a first or a last; and both of these 
are opposed to the nature of the infinite, which excludes every limit, whether it be a 
starting-point or a terminus. 

304. Now there is another point that must be noted, i.e., that if there are several intermediate 
parts in any finite thing, not all parts are intermediate to the same degree; for some are closer 
to what is first, and some to what is last. But in the case of some infinite thing in which there 
is neither a first nor last part, no part can be closer to or farther away from either what is first 
or what is last. Therefore all parts are intermediates to the same degree right down to the one 
you designate now. Consequently, if the causes of motion proceed to infinity in this way, 
there will be no first cause. But a first cause is the cause of all things. Therefore it will follow 
that all causes are eliminated; for when a cause is removed the things of which it is the cause 
are also removed. 

305. Neither is it possible (154) 

He shows that it is impossible to proceed to infinity in the case of material causes. First 
(154:C 300, he states what he intends to prove. Second (155:C 308), he proceeds with his 
proof ("Now there are two ways"). 

In regard to the first it must be noted that a patient is subjected to the action of an agent. 
Therefore to pass from agent to agent is to proceed in an upward direction, whereas to pass 
from patient to patient is to proceed in a downward direction. Now just as action is attributed 
to the cause of motion, so is undergoing action attributed to matter. Therefore among the 
causes of motion the process is in an upward direction, whereas anion', g material causes the 
process is in a downward direction. Consequently, since he showed among moving causes 
that it is impossible to proceed to infinity, as it were, in an upward direction, he adds that it is 
impossible to proceed to infinity in a downward direction, i.e., in the process of material 
causes, granted that there is a starting-point in an upward direction among the causes of 
motion. 

306. He illustrates this by way of the process of natural bodies, which proceeds in a 
downward direction, as if we were to say that water comes from fire, earth from water, and so 
on to infinity. He uses this example in accordance with the opinion of the ancient 
philosophers of nature, who held that one of these elements is the source of the others in a 
certain order. 


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307. However, this can also be explained in another way, inasmuch as we understand that in 
the case of moving causes there are evident to the senses certain ultimate effects which do not 
move anything else. Therefore we do not ask if there is an infinite regress in the lower 
members of that class, but if there is an infinite regress in the higher ones. But in regard to the 
class of material causes, he assumes that there is one first cause which is the foundation and 
basis of the others; and he inquires whether there is an infinite regress in a downward 
direction in the process of those things which are generated from matter. The example which 
he gives illustrates this, because he does not say that fire comes from water and this in turn 
from something else, but the converse, i.e., that water comes from fire, and something else 
again from this. For this reason first matter is held to exist; and he asks whether the things 
that are generated from matter proceed to infinity. 

308. Now there are two ways in which (155) 

He proves his original thesis. Concerning this he does four things. First (155:C 308), he 
distinguishes between the two ways in which one thing comes from something else. Second 
(156:C 31o), he shows that these two ways differ in two respects ("We say, then, that a 
man"). Third (158:C 312), he shows that it is impossible to proceed to infinity in either of 
these ways ("Now in neither way"). Fourth (159:C 314), he shows in which of these ways 
other things come from the first material principle ("At the same time"). 

He says, first, that one thing "comes from" another properly and essentially in two ways. He 
speaks thus in order to exclude that way in which something is said in an improper sense to 
come from something else only by reason of the fact that it comes after it as when it is said 
that certain feasts of the Greeks called the Olympian come from those called the Isthmian, or 
as we were to say that the feast of Epiphany comes from the the Nativity. But this is an 
improper use of the word, because the process of coming to be is a change, and in a change it 
is not only necessary that an order exist between the two limits of the change but also that 
both limits have the same subject. Now this is not the case in the above example, but we 
speak in this way insofar as we think of time as the subject of different feasts. 

309. Now properly speaking it is necessary to say that one thing comes from something else 
when some subject is changed from this into that. This occurs in two ways: first, as when we 
say that a man comes from a boy in the sense that a boy is changed from boyhood to 
manhood; second, as when we say that air comes from water as a result of substantial change. 

310. We say, then, that a man (156). 

He explains the twofold sense in which these two ways differ. First, we say that a man comes 
from a boy in the sense that what has already come into being comes from what is coming 
into being, or in the sense that what has already been completed comes from what is being 
completed. For anything in a state of becoming and of being completed is midway between 
being and non-being, just as generation is midway between existence and nonexistence. 
Therefore, since we reach an extreme through an intermediate, we say that what has been 
generated comes from what is being generated, and that what has been completed comes from 
what is being completed. Now this is the sense in which we say that a man comes from a boy, 
or a man of science from a learner, because a learner is one who is becoming a man of 
science. But in the other sense, i.e., the one in which we say that water comes from fire, one 
of the limits of the change is not related to the other as a passage or intermediate, as 
generation is to being, but rather as the limit from which a thing starts in order to reach 
another limit. Therefore one comes from the other when the other is corrupted. 


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311. This is why changes (157) 

He infers another difference from the foregoing one. For since, in the first way, one thing is 
related to the other as generation is to being, and as an intermediate to a limit, it is evident 
that one is naturally ordained to the other. Therefore they are not reversible so that one comes 
from the other indifferently. Consequently we do not say that a boy comes from a man, but 
the reverse. The reason for this is that those two things, of which one is said to come from the 
other in this way, are not related to each other in the same way as the two limits of a change, 
but as two things one of which comes after the other in sequence. And this is what he means 
when he says that "what has come into being" (i.e., the terminus of generation or being) does 
not come from generation as though generation itself were changed into being, but is that 
which exists after generation, because it follows generation in a natural sequence; just as 
one's destination comes after a journey, and as what is last comes after what is intermediate. 
Therefore, if we consider these two things, i.e., generation and being, the way in which they 
are related does not differ from the one we have excluded, in which sequence alone is 
considered, as when we say that the day comes from the dawn because it comes after the 
dawn. Moreover, this natural sequence prevents us from saying in an opposite way that the 
dawn comes "from the day," i.e., after the day; and for the same reason a boy cannot come 
from a man. But in the other sense in which one thing comes from another, the process is 
reversible; for just as water is generated by reason of air being corrupted, in a similar way air 
is generated by reason of water being corrupted. The reason is that these two are not related to 
each other in a natural sequence, i.e., as an intermediate to a limit, but as two limits, either 
one of which can be first or last. 

312. Now in neither way (158). 

He shows that it is impossible to proceed to infinity in either of these ways. First, in the way 
in which we say that a man comes from a boy; for the thing from which we say something 
else comes as a man comes from a boy has the position of an intermediary between two 
limits, i.e., between being and non-being. But an infinite number of intermediates cannot exist 
when certain limits are held to exist, since limits are opposed to infinity. Therefore, it is 
impossible to have an infinite series in this way. 

313. In like manner it is impossible to have an infinite series in the other way; for in that way 
one limit is con; verted into the other, because the corruption of one is the generation of the 
other, as has been explained. Now wherever a reversible process exists there is a return to 
some first thing in the sense that what was av first a starting-point is afterwards a terminus. 
This cannot occur in the case of things that are infinite, in which there is neither a 
starting-point nor a terminus. Consequently, there is no way in which one thing can come 
from another in an infinite regress. 

314. At the same time it is impossible (159). 

He shows in which of these ways something comes from first matter. Now it must be noted 
that in this place Aristotle uses two common suppositions accepted by all of the ancient 
philosophers: first, that there is a primary material principle, and therefore that in the process 
of generation there is no infinite regress on the part of the higher, i.e., of that from which a 
thing is generated; second, that matter is eternal. Therefore, from this second supposition he 
immediately concludes that nothing comes from first matter in the second way, i.e., in the 
way in which water comes from air as a result of the latter' s corruption, because what is 
eternal cannot be corrupted. 


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315. But since someone could say that the philosophers did not hold that the first material 
principle is eternal because it remains numerically one eternally but because it is eternal by 
succession (as if the human race were held to be eternal), he therefore excludes this from the 
first supposition. He says that since generation is not infinite in an upward direction but stops 
at a first material principle, then if there is a first material principle by reason of whose 
corruption other things come into being, it must not be the eternal principle of which the 
philosophers speak. The reason is that the first material principle cannot be eternal if other 
things are generated by reason of its corruption, and it in turn is generated by the corruption 
of something else. It is evident, then, that a thing comes from this first material principle as 
something imperfect and potential which is midway between pure nonbeing and actual being, 
but not as water comes from air by reason of the latter' s corruption. 


LESSON 4 

The Existence of a First in Final and Formal Causes 
ARISTOTLE'S TEXT Chapter 2: 994b 9-994b 31 

160. Again, that for the sake of which something comes to be is an end. Now such a thing is 
not for the sake of something else, but other things are for its sake. Therefore, if there is such 
a thing as an ultimate end, there will not be an infinite regress; but if there is no ultimate end, 
there will be no reason for which things come to be. 

161. Now those who posit infinity do away with the nature of the good without realizing it. 

162. But no one will attempt to do anything unless he thinks he can carry it through to its 
term. 

163. Nor will there be any intelligence in such matters, because one who has intelligence 
always acts for the sake of something since this limit is the end of a thing. 

164. Nor can the quiddity be reduced to a definition which adds to the defining notes. 

165. For a prior definition is always more of a definition, whereas a subsequent one is not; 
and where the first note does not apply, neither does a later one. 

166. Again, those who speak in this way do away with science, because it is impossible to 
have science until we reach what is undivided. 

167. Nor will knowledge itself exist; for how can one understand things which are infinite in 
this way? 

168. This case is not like that of a line, whose divisibility has no limit, for it would be 
impossible to understand a line if it had no limits. This is why no one will count the sections, 
which proceed to infinity. 

169. But it is necessary to understand that there is matter in everything that is moved, and that 
the infinite involves nothingness, but essence does not. But if there is no infinite, what 


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essence [i.e., definition] does the infinite have? 

170. Again, if the classes of causes were infinite in number, it would also be impossible to 
know anything; for we think that we have scientific knowledge when we know the causes 
themselves of things; but what is infinite by addition cannot be traversed in a finite period of 
time. 

COMMENTARY 

316. Having shown that there is no infinite regress either among the causes of motion or 
among material causes, the Philosopher now shows that the same thing is true of the final 
cause, which is called "that for the sake of which" something comes to be (160). 

He proves this by four arguments. The first is as follows. That for the sake of which 
something comes to be has the character of an end. But an end does not exist for the sake of 
other things, but others exist for its sake. Now such a thing either exists or not. If there is 
something of such a kind that all things exist for its sake and not it for the sake of something 
else, it will be the last thing in this order; and thus there will not be an infinite regress. 
However, if no such thing exists, no end will exist; and thus the class of cause called "that for 
the sake of which" will be eliminated. 

317. Now those who posit infinity (161). 

He gives the second argurgent, which is derived from the foregoing one; for from the first 
argument he concluded that those who posit an infinite regress in final causes do away with 
the final cause. Now when the final cause is removed, so also is the nature and notion of the 
good; because good and end have the same meaning, since the good is that which all desire, 
as is said in Book I of the Ethics. Therefore those who hold that there is an infinite regress in 
final causes do away completely with the nature of the good, although they do not realize this. 

318. But no one will attempt (162). 

He gives the third argument, which is as follows. If there were an infinite number of final 
causes, no one could reach a last terminus, because there is no last terminus in an infinite 
series. But no one will attempt to do anything unless he thinks he is able to accomplish 
something as a final goal. Therefore, those who hold that final causes proceed to infinity do 
away with every attempt to operate and even with the activities of natural bodies; for a thing's 
natural movement is only toward something which it is naturally disposed to attain. 

319. Nor will there be (163). 

He states the fourth argument, which is as follows. One who posits an infinite number of final 
causes does away with a limit, and therefore with the end for the sake of which a cause acts. 
But every intelligent agent acts for the sake of some end. Therefore it would follow that there 
is no intellect among causes which are productive; and thus the practical intellect is 
eliminated. But since these things are absurd, we must reject the first position, from which 
they follow, i.e., that there is an infinite number of final causes. 

320. Nor can the quiddity (164). 


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He shows that there is not an infinite number of formal causes. In regard to this he does two 
things. First (164:C 320), he states what he intends to prove. Second (165:C 322), he proves it 
("For a prior definition"). 

Regarding the first we must understand that each thing derives its particular species from its 
proper form, and this is why the definition of a species signifies chiefly a thing's form. 
Therefore we must understand that a procession of forms is consequent upon a procession of 
definitions; for one part of a definition is prior to another just as genus is prior to difference 
and one difference is prior to another. Therefore an infinite regress in forms and in the parts 
of a definition is one and the same thing. Now since Aristotle wishes to show that it is 
impossible to proceed to infinity in the case of formal causes, he holds that it is impossible to 
proceed to infinity in the parts of a definition. Hence he says that it is impossible for a thing's 
quiddity to be reduced to another definition, and so on to infinity, so that the defining notes 
are always increased in number. For example, one who defines man gives animal in his 
definition, and therefore the definition of man is reduced to that of animal, and this in turn to 
the definition of something else, thereby increasing the defining notes. But to proceed to 
infinity in this way is absurd. 

321. Now we do not mean by this that there are the same number of forms in each individual 
as there are genera and differences, so that in man there is one form by which he is man, 
another by which he is animal, and so on; but we mean that there must be as many grades of 
forms in reality as there are orders of genera and differences [in knowledge]. For we find in 
reality one form which is not the form of a body, another which is the form of a body but not 
of an animated body, and so on. 

322. For a prior definition (165). 

He proves his premise by four arguments. The first is this. Wherever there are a number of 
forms or defining notes, a prior definition is always "more of a definition." This does not 
mean that a prior form is more complete (for specific forms are complete), but that a prior 
form belongs to more things than a subsequent form, which is not found wherever a prior 
form is found; e.g., the definition of man is not found wherever that of animal is found. From 
this he argues that if the first note [of a series] does not fit the thing defined, "neither does a 
later one." But if there were an infinite regress in definitions and forms, there would be no 
first definition or definitive form. Hence all subsequent definitions and forms would be 
eliminated. 

323. Again, those who speak (166). 

He gives the second argument, which is as follows. It is impossible to have scientific 
knowledge of anything until we come to what is undivided. Now in this place "undivided" 
cannot mean the singular, because there is no science of the singular. However, it can be 
understood in two other ways. First, it can mean the definition itself of the last species, which 
is not further divided by essential differences. In this sense his statement can mean that we do 
not have complete knowledge of a thing until we reach its last species; for one who knows the 
genus to which a thing belongs does not yet have a complete knowledge of that thing. 
According to this interpretation we must say that, just as the first argument concluded that it 
is impossible to have an infinite regress in an upward direction among formal causes, in a 
similar fashion this second argument concludes that it is impossible to have an infinite regress 
in a downward direction, otherwise it would be impossible to reach a last species. Therefore 
this position destroys any complete knowledge. 


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324. Now a formal division exists not only when a genus is divided by differences (and when 
such division is no longer possible the last species can be said to be undivided), but also when 
the thing defined is divided into its definitive parts, as is evident in Book I of the Physics. 
Therefore in this place "undivided" can also mean a thing whose definition cannot be 
resolved into any definitive parts. Now according to this the supreme genus is undivided; and 
from this point of view his statement can mean that we cannot have scientific knowledge of a 
thing by definition unless we reach its supreme genera; because when these remain unknown 
it is impossible to know its subsequent genera. And according to this the second argument 
concludes, as the former one did, that it is impossible to proceed to infinity in an upward 
direction among formal causes. 

325. Or, in order to reach the same conclusion, "undivided" can be explained in another way, 
i.e., in the sense that an immediate proposition is undivided. For if it were possi ' hie to 
proceed to infinity in an upward direction in the case of definitions, there would be no 
immediate proposition, and thus science as such, which is about conclusions derived from 
immediate principles, would be destroyed. 

326. Nor will knowledge (167) 

He gives the third argument, which proceeds to [show that such an infinite regress would] 
destroy not only science but any kind of human knowing whatsoever. In regard to this 
argument he does two things. First (167:C 326), he gives his argument. Second (168:C 327), 
he refutes an objection raised against it ("This case is not like"). 

The argument is as follows. We know each thing by understanding its form. But if there were 
an infinite regress in forms, these forms could not be understood, because the intellect is 
incapable of understanding the infinite as infinite. Therefore this position destroys knowing in 
its entirety. 

327. This case is not like (168). 

He disposes of an objection; for someone could say that a thing having an infinite number of 
forms can be understood in the same way as a line which is divided to infinity. But he denies 
this. He says that this case is not the same as that of a line, whose divisions do not stop but go 
on to infinity. For it is impossible to understand anything unless some limit is set to it. 
Therefore a line can be understood inasmuch as some actual limit is given to it by reason of 
its extremes. However, it cannot be understood insofar as its division does not terminate. 
Hence no one can count the divisions of a line insofar as they are infinite. But as applied to 
forms "infinite" means actually infinite, and not potentially infinite as it does when applied to 
the division of a line. Therefore, if there were an infinite number of forms, there would be no 
way in which a thing could be known either scientifically or in any way at all. 

328. But it is necessary (169). 

He gives the fourth argument, which runs thus. Matter must be understood to exist in 
everything that is moved; for whatever is moved is in potentiality, and what is in potentiality 
is matter. But matter itself has the character of the infinite, and nothingness belongs to the 
infinite in the sense of matter, because matter taken in itself is understood without any of kind 
of form. And since nothingness belongs to the infinite, it follows contrariwise that the 
principle by which the infinite is a being is itself not infinite, and that it does not belong "to 
the infinite," i.e., to matter, to be infinite in being. But things are by virtue of their form. 


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Hence there is no infinite regress among forms. 

329. However, it must be noted that in this place Aristotle holds that the infinite involves the 
notion of nothingness, not because matter involves the notion of privation (as Plato claimed 
when he failed to distinguish between privation and matter), but because the infinite involves 
the notion of privation. For a potential being contains the notion of the infinite only insofar as 
it comes under the nature of privation, as is evident in Book III of the Physics. 

330. Again, if the classes (170). 

He shows that the classes of causes are not infinite in number, and he uses the following 
argument. We think that we have scientific knowledge of each thing when we know all its 
causes. But if there were an infinite number of causes in the sense that one class of cause may 
be added to another continuously, it would be impossible to traverse this infinity in such a 
way that all causes could be known. Hence in this way too the knowing of things would be 
destroyed. 


LESSON 5 

The Method to Be Followed in the Search for Truth 
ARISTOTLE'S TEXT Chapter 3: 994b 32-995a 20 

171. The way in which people are affected by what they hear depends upon the things to 
which they are accustomed; for it is in terms of such things that we judge statements to be 
true, and anything over and above these does not seem similar but less intelligible and more 
remote. For it is the things to which we are accustomed that are better known. 

172. The great force which custom has is shown by the laws, in which legendary and childish 
elements prevail over our knowledge of them, because of custom. 

173. Now some men will not accept what a speaker says unless he speaks in mathematical 
terms; and others, unless he gives examples; while others expect him to quote a poet as an 
authority. Again, some want everything stated with certitude, while others find certitude 
annoying, either because they are incapable of comprehending anything, or because they 
consider exact inquiry to be quibbling; for there is some similarity. Hence it seems to some 
men that, just as liberality is lacking in the matter of a fee for a banquet, so also is it lacking 
in arguments. 

174. For this reason one must be trained how to meet every kind of argument; and it is absurd 
to search simultaneously for knowledge and for the method of acquiring it; for neither of 
these is easily attained. 

175. But the exactness of mathematics is not to be expected in all cases, but only in those 
which have no matter. This is why its method is not that of natural philosophy; for perhaps 
the whole of nature contains matter. Hence we must first investigate what nature is; for in this 
way it will become evident what the things are with which natural philosophy deals, and 
whether it belongs to one science or to several to consider the causes and principles of things. 


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COMMENTARY 

33 1 . Having shown that the study of truth is in one sense difficult and in another easy, and 
that it belongs preeminently to first philosophy, the Philosopher now exposes the proper 
method of investigating the truth. In regard to this he does two things. First (171:C 331), he 
gives the different methods which men follow in the study of truth. Second (335), he shows 
which method is the proper one ("For this reason one must"). 

In regard to the first he does two things. First, he shows how powerful custom is in the study 
of truth. Second (172:C 333), he makes this clear by an example ("The great force"). 

He says, first, that the way in which people are affected by what they hear depends upon the 
things to which they are accustomed, because such things are more willingly heard and more 
easily understood. For things spoken of in a manner to which we are accustomed seem to us 
to be acceptable; and if any things are said to us over and above what we have been 
accustomed to hear, these do not seem to have the same degree of truth. As a matter of fact 
they seem less intelligible to us and further removed from reason just because we are not 
accustomed to them; for it is the things which we are accustomed to hear that we know best of 
all. 

332. Now the reason for this is that things which are customary become natural. Hence a 
habit, which disposes us in a way similar to nature, is also acquired by customary activity. 
And from the fact that someone has some special sort of nature or special kind of habit, he 
has a definite relationship to one thing or another. But in every kind of cognition there must 
be a definite relationship between the knower and the object of cognition. Therefore, to the 
extent that natures and habits differ, there are diverse kinds of cognition. For we see that there 
are innate first principles in men because of their human nature, and that what is proper to 
some special virtue appears good to one who has this habit of virtue; and, again, that 
something appears palatable to the sense of taste because of its disposition. Therefore, since 
custom produces a habit which is similar to nature, it follows that what is customary is better 
known. 

333. The great force (172)> 

Here he makes his previous statement clear by giving a concrete case. He says that the laws 
which men pass are positive evidence of the force of custom; for the legendary and childish 
elements in these laws are more effective in winning assent than is knowledge of the truth. 
Now the Philosopher is speaking here of the laws devised by men, which have as their 
ultimate end the preservation of the political community. Therefore the men who have 
established these laws have handed down in them, in keeping with the diversity of peoples 
and nations involved, certain directives by which human souls might be drawn away from 
evil and persuaded to do good, although many of them, which men had heard from childhood 
and of which they approved more readily than of what they knew to be true, were empty and 
foolish. 

But the law given by God directs men to that true happiness to which everything false is 
opposed. Therefore there is nothing false in the divine law. 

334. Now some men (173). 


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Here he shows how men as a result of custom use different methods in the study of truth. He 
says that some men listen to what is said to them only if it is mathematical in character; and 
this is acceptable to those who have been educated in mathematics because of the habits 
which they have. Now since custom is like nature, the same thing can also happen to certain 
men (1) because they are poorly disposed in some respect, e.g., those who have a strong 
imagination but little intelligence. (2) Then there are others who do not wish to accept 
anything unless they are given a concrete example, either because they are accustomed to this 
or because their sensory powers dominate and their intellect is weak. (3) Again, there are 
some who think that nothing is convincing enough unless a poet or some authority is cited. 
This is also a result either of custom or of poor judgment, because they cannot decide for 
themselves whether the conclusion of an argument is certain; and therefore, having no faith in 
their own judgment, as it were, they require the judgment of some recognized authority. (4) 
Again there are others who want everything said to them with certitude, i.e., by way of careful 
rational investigation. This occurs because of the superior intelligence of the one making the 
judgment and the arguments of the one conducting the investigation, provided that one does 
not look for certitude where it cannot be had. (5) On the other hand there are some who are 
annoyed if some matter is investigated in an exact way by means of a careful discussion. This 
can occur for two reasons, (a) First, they lack the ability to comprehend anything; for since 
their reasoning power is poor they are unable to understand the order in which premises are 
related to conclusions, (b) Second, it occurs because of quibbling, i.e., reasoning about the 
smallest matters, which bears some resemblance to the search for certitude since it leaves 
nothing undiscussed down to the smallest detail, (c) Then there are some who think that, just 
as liberality is lacking when the smallest details are taken into account in estimating the fee 
for a banquet, in a similar way there is a lack of civility and liberality when a man also wishes 
to discuss the smallest details in the search for truth. 

335. For this reason one must be trained (174). 

He exposes the proper method of investigating the truth. Concerning this he does two things. 
First ( 335), he shows how a man can discover the proper method of investigating the truth. 
Second (336), he explains that the method which is absolutely the best should not be 
demanded in all matters ("But the exactness of mathematics") . 

He says, first, that since different men use different methods in the search for truth, one must 
be trained in the method which the particular sciences must use to investigate their subject. 
And since it is not easy for a man to undertake two things at once (indeed, so long as he tries 
to do both he can succeed in neither), it is absurd for a man to try to acquire a science and at 
the same time to acquire the method proper to that science. This is why a man should learn 
logic before any of the other sciences, because logic considers the general method of 
procedure in all the other sciences. Moreover, the method appropriate to the particular 
sciences should be considered at the beginning of these sciences. 

336. But the exactness of mathematics (175). 

He shows that the method which is absolutely the best should not be demanded in all the 
sciences. He says that the "exactness," i.e., the careful and certain demonstrations, found in 
mathematics should not be demanded in the case of all things of which we have science, but 
only in the case of those things which have no matter; for things that have matter are subject 
to motion and change, and therefore in their case complete certitude cannot be had. For in the 
case of these things we do not look for what exists always and of necessity, but only for what 
exists in the majority of cases. 


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Now immaterial things are most certain by their very nature because they are unchangeable, 
although they are not certain to us because our intellectual power is weak, as was stated above 
(279). The separate substances are things of this kind. But while the things with which 
mathematics deals are abstracted from matter, they do not surpass our understanding; and 
therefore in their case most certain reasoning is demanded. 

Again, because the whole of nature involves matter, this method of most certain reasoning 
does not belong to natural philosophy. However, he says "perhaps" because of the celestial 
bodies, since they do not have matter in the same sense that lower bodies do. 

337. Now since this method of most certain reasoning is not the method proper to natural 
science, therefore in order to know which method is proper to that science we must 
investigate first what nature is; for in this way we will discover the things which natural 
philosophy studies. Further, we must investigate "whether it belongs to one science," i.e., to 
natural philosophy, or to several sciences, to consider all causes and principles; for in this 
way we will be able to learn which method of demonstration is proper to natural philosophy. 
He deals with this method in Book II of the Physics, as is obvious to anyone who examines it 
carefully. 


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METAPHYSICS 
BOOK III 

METAPHYSICAL PROBLEMS 

CONTENTS 

The Need of Questioning Everything in the Search for Universal Truth 

Questions Concerning the Method of This Science 

Questions Concerning the Things with Which This Science Deals 

Are All the Classes of Causes Studied by One Science or by Many? 

Are the Principles of Demonstration and Substance Considered by One 
Science or by Many? 

Are All Substances Considered by One Science or by Many? Does the 
Science of Substance Consider the Essential Accidents of Substance? 

Are There Certain Other Substances Separate from Sensible Things? 
Criticism of the Different Opinions Regarding the Objects of Mathematics 

Are Genera Principles of Things? And If So, Does This Apply to The Most 
Universal Genera or to Those Nearest to Individuals? 

Do Any Universals Exist Apart from the Singular Things Perceived by the 
Senses and from Those Which Are Composed of Matter and Form? 

Do All Things Have a Single Substance? Do All Things Have the Same or 
Different Principles? 

Do Corruptible and Incorruptible Things Have the Same or Different 
Principles? 

Are Unity and Being the Substance and Principle of All Things? 

Are Numbers and Continuous Quantities the Substances and Principles of 
Sensible Things? 

Are There Separate Forms in Addition to the Objects of Mathematics and 
Sensible Things? 

Do First Principles Exist Actually or Potentially, and Are They Universal or 
Singular? 

LESSON I 

The Need of Questioning Everything in the 8earch for Universal Truth 
ARISTOTLE'S TEXT Chapter 1: 995a 24-995b 4 

176. With a view to the science under investigation we must attack first those subjects which 
must first be investigated. These are all the subjects about which some men have entertained 
different opinions, and any other besides these which has been omitted. 


LESSON 1: 
LESSON 2 
LESSON 3 
LESSON 4 

LESSON 5 

LESSON 6 

LESSON 7 

LESSON 8 

LESSON 9 

LESSON 10 

LESSON 11 
LESSON 12 
LESSON 13 

LESSON 14 

LESSON 15 


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177. Now for those who wish to investigate the truth it is worth the while to ponder these 
difficulties well. For the subsequent study of truth is nothing else than the solution of earlier 
problems. For it is impossible to untie a knot without knowing it. But a perplexity on the part 
of the mind makes this evident in regard to the matter at hand; for insofar as the mind is 
perplexed, to that extent it experiences something similar to men who are bound; for in both 
cases it is impossible to move forward. For this reason, then, it is first necessary to consider 
all the difficulties and the reasons for them. 

178. [This is also necessary] for another reason, namely, that those who make investigations 
without first recognizing the problem are like those who do not know where they ought to go. 

179. Again, one would not even know when he finds the thing which he is seeking [and when 
not] ; for the goal is not evident to such a man, but it is evident to one who previously 
discussed the difficulties. 

180. Furthermore, one who has heard all the arguments of the litigants, as it were, and of 
those who argue the question, is necessarily in a better position to pass judgment. 

COMMENTARY 

338. Having indicated in Book II (331) the method of considering the truth, the Philosopher 
now proceeds with his study of the truth. First he proceeds disputatively, indicating those 
points which are open to question so far as the truth of things is concerned. Second (529), he 
begins to establish what is true, and he does this in Book IV, which begins: "There is a certain 
science." 

The first part is divided into two sections. In the first, he states what he intends to do. In the 
second (346), he proceeds to do it ("The first problem"). 

In regard to the first he does two things. First, he states what he intends to do. Second (339), 
he gives the reasons for this ("Now for those"). 

He says first, then, that with a view to this science which we are seeking about first principles 
and what is universally true of things, we must attack, first of all, those subjects about which 
it is necessary to raise questions before the truth is established. Now there are disputed points 
of this kind for two reasons, either because the ancient philosophers entertained a different 
opinion about these things than is really true, or because they completely neglected to 
consider them. 

339. Now for those (177). 

Here he gives four arguments in support of this thesis: 

First, he says that for those who wish to investigate the truth it is "worth the while," i.e., 
worth the effort, "to ponder these difficulties well," i.e., to examine carefully those matters 
which are open to question. This is necessary because the subsequent study of truth is nothing 
else than the solution of earlier difficulties. Now in loosening a physical knot it is evident that 
one who is unacquainted with this knot cannot loosen it. But a difficulty about some subject is 
related to the mind as a physical knot is to the body, and manifests the same effect. For 
insofar as the mind is puzzled about some subject, it experiences something similar to those 
who are tightly bound. For just as one whose feet are tied cannot move forward on an earthly 


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road, in a similar way one who is puzzled, and whose mind is bound, as it were, cannot move 
forward on the road of speculative knowledge. Therefore, just as one who wishes to loosen a 
physical knot must first of all inspect the knot and the way in which it is tied, in a similar way 
one who wants to solve a problem must first survey all the difficulties and the reasons for 
them. 

340. [This is also necessary] (178). 

Here he gives the second argument. He says that those who wish to investigate the truth 
without first considering the problem are like those who do not know where they are going. 
This is true for this reason, that, just as the terminus of a journey is the goal intended by one 
who travels on foot, in a similar way the solution of a problem is the goal intended by one 
who is seeking the truth. But it is evident that one who does not know where he is going 
cannot go there directly, except perhaps by chance. Therefore, neither can one seek the truth 
directly unless he first sees the problem. 

341. Again, one would (179). 

Here he gives the third argument. He says that, just as one who is ignorant of where he is 
going does not know whether he should stop or go further when he reaches his appointed 
goal, in a similar way one who does not know beforehand the problem whose solution marks 
the terminus of his search cannot know when he finds the truth which he is seeking and when 
not. For he does not know what the goal of his investigations is, but this is evident to one who 
knew the problem beforehand. 

342. Furthermore (180). 

He gives the fourth argument, which is taken from the viewpoint of a judge. For a judge must 
pass judgment on the things which he hears. But just as one can pass judgment in a lawsuit 
only if he hears the arguments on both sides, in a similar way one who has to pass judgment 
on a philosophy is necessarily in a better position to do so if he will hear all the arguments, as 
it were, of the disputants. 

343. Now it must be noted that it was for these reasons that Aristotle was accustomed, in 
nearly all his works, to set forth the problems which emerge before investigating and 
establishing what is true. But while in other works Aristotle sets down the problems one at a 
time in order to establish the truth about each one, in this work he sets forth all the problems 
at once, and afterwards in the proper order establishes the things that are true. The reason for 
this is that other sciences consider the truth in a particular way, and therefore it belongs to 
them to raise problems of a particular kind about individual truths. But just as it belongs to 
this science to make a universal study of truth, so also does it belong to it to discuss all the 
problems which pertain to the truth. Therefore it does not discuss its problems one at a time 
but all at once. 

344. There can also be another reason [why Aristotle proceeds in this way], namely, that 
those problems on which he touches are chiefly those about which the philosophers have held 
different opinions. However, he does not proceed to investigate the truth in the same order as 
the other philosophers did. For he begins with things which are sensible and evident and 
proceeds to those which are separate from matter, as is evident below in Book VII (1566), 
whereas the other philosophers wanted to apply intelligible and abstract principles to sensible 
things. Hence, because he did not intend to establish the truth in the same order as that 


METAPHYSICAL PROBLEMS 


Thomas Aquinas: Commentary on Aristotle's Metaphysics: English 

followed by the other philosophers, and from whose views these problems arise, he therefore 
decided to give first all the problems in a separate section, and afterwards to solve these 
problems in their proper order. 

345. Averroes gives another reason [for Aristotle's procedure]. He says that Aristotle 
proceeds in this way because of the relationship of this science to logic, which will be 
touched on below in Book IV (588); and therefore he made dialectical discussion a principal 
part of this science. 


LESSON 2 

Questions Concerning the Method of This Science 
ARISTOTLE'S TEXT Chapter 1: 995b 4-995b 27 

181. The first problem concerns the things about which we raised questions in our 
introductory statements, i.e., whether it belongs to one science or to many to speculate about 
the causes. 

182. And there is also the problem whether it belongs to this science to know only the 
principles of substance, or also the principles on which all sciences base their demonstrations, 
e.g., whether it is possible to affirm and deny one and the same thing at the same time or not; 
and other such principles. And if this science deals with substance, there is the question 
whether one science deals with all substances, or many sciences. And if many, whether all are 
cognate, or whether some should be called wisdom and others something else. 

183. It is also necessary to inquire whether sensible substances alone must be said to exist, or 
whether there are other substances in addition to these; and whether they are unique, or 
whether there are many classes of substances, aswas claimed by those who created the Forms 
and made the objects of mathematics an intermediate class between these Forms and sensible 
substances. As we have said, then, it is necessary to examine these questions. 

184. There is also the problem whether this speculation has to do with substances alone or 
also with the proper accidents of substances. And we must inquire about sameness and 
difference, likeness and unlikeness, contrariety, priority and posteriority, and all other such 
things which the dialecticians attempt to treat (basing their investigations only on 
probabilities); for to them too it belongs to theorize about all these things. Furthermore, we 
must investigate all those essential accidents of these same things; and not only what each one 
of them is, but also whether there is one contrary for each one. 

COMMENTARY 

Q. 1: Does this science make use of all four causes? 

346. Following out his announced plan, the Philosopher begins to set down the problems 
which are encountered in establishing the truth; and he divides this into two parts. In the first, 
he gives these problems; and in the second (369), he gives the reasons for these problems, by 
indicating the arguments on either side of the question ("Therefore let us discuss"). 


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Now it was stated in Book II (335) that it is necessary to seek the method of a science before 
seeking the science itself. Therefore he gives, first, the problems which pertain to this 
science's method of investigation. Second (355), he gives the problems which pertain to the 
first principles with which this science deals, as has been stated in Book I (36) ("And we must 
inquire"). 

Now a science is concerned with two things, as was said in Book II (336), namely, a study of 
the causes by which it demonstrates and the things with which it deals. Hence in regard to the 
first point he does two things. First, he presents a problem concerning the investigation of 
causes. Second (347), he presents several problems concerning the things with which this 
science deals ("And there is also the problem") 

He says, then, that the first problem is one which we proposed in the issues raised at the end 
of Book II (336), which is, so to speak, the prologue to the whole of science, i.e., whether a 
study of the four causes in their four classes belongs to one science or to many different 
sciences And this is to ask whether it belongs to one science, and especially to this science, to 
demonstrate by means of all the causes, or rather whether some sciences demonstrate by one 
cause and some by another. 

Q. 2: Does it consider both principles of substance and principles of knowledge? 

347. And there is also the problem (182). 

Here he raises problems about the things which this science considers. First, he inquires about 
the things which this science considers about substances; and second (350), about substances 
themselves ("It is also necessary"). In regard to the first he raises three questions. For if it is 
supposed, from what was said in Book I (35), that this science considers first principles, the 
first question here will be whether it belongs to this science to know only the first principles 
of substances, or also to consider the first principles of demonstration, by means of which all 
sciences demonstrate. For example, should this science consider whether it is possible to 
affirm and deny one and the same thing at the same time or not? And the same thing applies 
to the other first and self-evident principles of demonstration. 

Q. 3: Is its subject all substances, or do different sciences consider different substances? 

348. And if this science considers substance as the primary kind of being, the second question 
is whether there is one science which considers all substances, or whether there are many 
sciences which consider different substances. For it seems that there should be many sciences 
which consider many substances. 

Q. 4: Is it distinct from other sciences? 

349. And if there are many sciences which consider many substances, the third question is 
whether all are "cognate," i.e., whether all belong to one class, as geometry and arithmetic 
belong to the class of mathematical science, or whether they do not, but some to the class of 
wisdom and some to another class, for example, to the class of natural philosophy or to that of 
mathematical science. For according to the first point of view it seems that they do not belong 
to one class, since material and immaterial substances are not known by the same method. 

Q. 5. Are there immaterial substances, and of what kind? 


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350. It is also necessary (183). 

Here he adds to the number of questions about substance; and he does this by raising two 
questions. The first question is whether sensible substances alone must be held to exist, as the 
philosophers of nature claimed, or whether there are in addition to sensible substances other 
immaterial and intelligible substances, as Plato claimed. 

351. And if there are some substances separate from sensible things, the second question is 
whether "they are unique," i.e., whether they belong only to one class, or whether there are 
many classes of such substances. For certain men, understanding that there is a twofold 
abstraction, namely, of the universal from the particular, and of the mathematical form from 
sensible matter, held that each class is self-subsistent. Thus they held that there are separate 
substances which are subsisting abstract universals, and between these and particular sensible 
substances they placed the objects of mathematics — numbers, continuous quantities, and 
figures — which they regarded as separate subsisting things. Concerning the questions which 
have now been raised, then, it is necessary to investigate them below. He does this, first, by 
arguing both sides of the question, and, second, by determining its truth. 

Q. 6: Does this science consider accidents or properties of substance? 

352. There is also the problem (184). 

Here he asks whether this science's investigations extend to accidents; and he raises three 
questions. The first is whether this science, seeing that it is called the philosophy of 
substance, speculates about substance alone, or whether it also speculates about the proper 
accidents of substance; for it seems to be the office of the same science to consider a subject 
and the proper accidents of that subject. 

Q. 7: How does it differ from logic in considering these things? 

353. The second question is whether this science considers certain things which seem to be 
proper accidents of being and which belong to all beings, namely, sameness and difference, 
likeness and unlikeness, contrariety, priority, and posteriority, and all others of this kind 
which are treated by the dialecticians, who deal with all things. However, they do not 
examine such things according to necessary premises but according to probable ones. For 
from one point of view it seems that, since these accidents are common ones, they pertain to 
first-philosophy; but from another point of view it seems that, since they are considered by 
the dialecticians, whose office it is to argue from Probabilities, an examination of them does 
not belong to the consideration of the philosopher, whose office it is to demonstrate. 

Q. 8: Does it consider how these accidents are inter-related? 

354. And since certain proper attributes naturally flow from these common accidents of 
being, the third question is whether it is the function of the philosopher to consider in regard 
to the common accidents only their quiddity or also their properties; for example, whether 
there is one opposite for each one. 


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Questions Concerning the Things with Which This Science Deals 

ARISTOTLE'S TEXT Chapter 1: 995b 27-996a 17 

185. And we must inquire whether it is genera that constitute the principles and elements of 
things, or the parts into which each existing thing is divided. And if it is genera, whether it is 
those that are predicated of individuals first or last. And we must also inquire whether animal 
or man is a principle, and exists more truly than the singular. 

186. But most of all it is necessary to investigate and treat the question whether besides 
matter there is any cause in the proper sense or not; and whether it is separable or not; and 
whether it is numerically one or many. And we must ask whether there is anything besides the 
synolon (and by synolon I mean matter when something is predicated of it), or nothing; or 
whether this is true of some things but not of others, [and what these things are]. 

187. Further, we must inquire whether the principles of things are limited in number or in 
kind, both those in the intelligible structures of things and those in the underlying subject; and 
whether the principles of corruptible and of incorruptible things are the same or different; and 
whether they are all incorruptible, or whether those of corruptible things are corruptible. And 
the most difficult question of all, and the most disputed one, is whether unity and being are 
not something different from the substances of existing things, as the Pythagoreans and Plato 
say, or whether this is not the case, but the underlying subject is something different," as 
Empedocles holds of love, another thinker of fire, another of water, and another of air. And 
we must inquire whether the principles of things are universals or singular things. 

188. Again, we must inquire whether they exist potentially or actually. And also whether they 
are principles of things in some other way or in reference to motion; for these questions 
present great difficulty. 

189. And in addition to these questions we must inquire whether numbers or lengths and 
points are somehow substances or not. And if they are substances, whether they are separate 
from sensible things or are found in them. Concerning all these matters it is not only difficult 
to discover what is true, but it is not even easy to state the problems well. 

COMMENTARY 

Q. 9: How are substances to be analysed, into elements or into genera? 

355. Having raised questions pertaining to the method of investigation which this science 
uses, the Philosopher now raises questions pertaining to the things which this science 
considers. And since this science considers first principles, as has been stated in Book I (35), 
he therefore raises here questions pertaining to the principles of things. 

Now both the Forms and the objects of mathematics were held to be the first principles of 
things. Therefore, first, he raises questions concerning the Forms; and second (366), 
concerning the objects of mathematics ("And in addition to these"). 

In regard to the first he does two things. First, he asks what things are principles; and second 
(361), what sort of beings they are ("Further, we must inquire"). 


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And since separate universals were held to be the principles of things, he asks, first, whether 
universals are the principles of things; and second (357), whether separate entities are the 
principles of things ("But most of all"). 

Concerning the first he asks two questions. The first is whether genera constitute the 
principles and elements of things, or the ultimate parts into which each individual thing is 
dissolved. This question arises because an element is that of which a thing is first composed 
and into which it is ultimately dissolved. Now we find a twofold mode of composition and 
dissolution. One has to do with the intelligible constitution, in which species are resolved into 
genera, and according to this mode genera seem to be the principles and elements of things, as 
Plato claimed. The other mode of composition and dissolution has to do with the real order; 
for example, natural bodies are composed of fire, air, water and earth, and are dissolved into 
these. It was for this reason that the natural philosophers claimed that the elements constitute 
the first principles of things. 

356. And assuming that genera are the principles of things, the second question is whether the 
principles of things are to be identified with the universals which are predicated of individual 
things, i.e., the lowest species, which he calls genera after the usage of the Platonists, because 
the lowest species contain under themselves many individuals just as genera contain many 
species; or whether it is rather the first and most common genera that constitute principles, for 
example, which of the two is more of a principle, animal or man; for man is a principle 
according to the Platonists, and is more real than any singular man. Now this problem arises 
because of two divisions which reason makes. One of these is that whereby we divide genera 
into species, and the other is that whereby we resolve species into genera. For it seems that 
whatever is the last term in a process of division is always the first principle and element in a 
process of composition. 

Q. 10: Is there an immaterial principle? Is it one or many? 

357. But most of all (186). 

Here he inquires whether separate entities are the principles of things; and he raises four 
questions. For since the first philosophers of nature posited only a material cause, the first 
question is whether besides matter there is anything else that is a cause in the proper sense or 
not. 

358. And granted that there is some other cause besides matter, the second question is 
whether it is separable from matter, as Plato held, or as Pythagoras held. 

359. And if there is something separable from matter, the third question is whether it is a 
single thing, as Anaxagoras claimed, or many, as Plato and Aristotle himself claimed. 

Q. 11: Is individuality distinct from the specific form? 

360. The fourth question is whether there is anything "besides the synolon," i.e., the concrete 
whole, or nothing; or whether there is something in certain cases and not in others; and what 
kind of things they are in those cases in which there is something else, and what kind of 
things they are in those in which there is not. And he explains what a synolon or concrete 
whole is; i.e., it is matter when something is predicated of it. Now in order to understand this 
we must note that Plato claimed that man and horse, and universals which are predicated in 
this way, are certain separate Forms; and that man is predicated of Socrates or Plato by reason 


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of the fact that sensible matter participates in a separate Form. Hence Socrates or Plato is 
called a synolon or concrete whole, because each is constituted as a result of matter 
participating in a separate form. And each is, as it were, a kind of predicate of matter. Hence 
the Philosopher asks here whether the whatness of the individual thing is something else in 
addition to the individual thing itself, or not; or also whether it is something rise in the case of 
some things and not in that of others. The Philosopher will answer this question in Book VII 
(7356). 

361. Further, we must inquire (187). 

Here he raises questions about the way in which principles exist. And since being is divided 
by the one and many, and by act and potency, he asks, first, whether these principles are one 
or many; and second (365), whether they are actual or potential ("Again, we must inquire"). 
In regard to the first he asks four questions: 

Q. 12 The first is whether the principles of things are limited in number or in kind; as we say, 
for example, that there are three principles of nature. Now the statement that they are limited 
in number can mean that the principle of nature is numerically a single form and a single 
matter and privation. And the statement that they are limited in kind can mean that there are 
many material principles which have in common the specific nature of material principle, and 
so on for the rest. And since some of the philosophers, such as the Platonists, attributed 
formal causes to things, while others, such as the ancient natural philosophers, attributed only 
material causes to things, he adds that this question is applicable both "in the intelligible 
structures," i.e., in formal causes, "and in the underlying subject," i.e., in material causes. 

Q. 13: Are the principles of corruptible and incorruptible things the same or different? 

362. (2) The second question is whether the principles of corruptible and of incorruptible 
things are the same or different. And if they are different, whether all are incorruptible, or 
whether the principles of corruptible things are corruptible and those of incorruptible things 
are incorruptible. 

Q. 14: Are "one" and "being" the same as or distinct from specific natures? 

363. (3) The third question is whether unity and being signify the very substance of things 
and not something added to the substance of things, as the Pythagoreans and Platonists 
claimed; or whether they do not signify the substance of things, but something else is the 
subject of unity and being, for example, fire or air or something else of this kind, as the 
ancient philosophers of nature held. Now he says that this question is the most difficult and 
most puzzling one, because on this question depends the entire thought of Plato and 
Pythagoras, who held that numbers are the substance of things. 

364. The fourth question is whether the principles of things are "somehow universals or are in 
some sense singular things," i.e., whether those things which are held to be principles have 
the character of a principle in the sense of a universal intelligible nature, or according as each 
is a particular and singular thing. 

365. Again, we must inquire (188). 

Here he asks whether these principles exist potentially or actually. This question seems to 
refer especially to material principles; for it can be a matter of dispute whether the first 


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material principle is some actual body, such as fire or air, as the ancient philosophers of 
nature held, or something which is only potential, as Plato held. And since motion is the 
actualization of something in potency, and is, in a sense, midway between potentiality and 
actuality, he therefore adds another question: whether the principles of things are causes only 
in reference to motion, as the philosophers of nature posited only principles of motion, either 
material or efficient, or also whether they are principles which act in some other way than by 
motion, as Plato claimed that sensible things are caused by immaterial entities by a certain 
participation in these. Futhermore, he says that these questions have been raised because they 
present the greatest difficulty, as is clear from the manner in which the philosophers have 
disagreed about them. 

366. And in addition to these (189). 

Here he raises questions concerning the objects of mathematics, which are posited as the 
principles of things. He raises two questions. The first is whether numbers, lengths, figures 
and points are somehow substances, as the Pythagoreans or Platonists held, or whether they 
are not, as the philosophers of nature held. 

367. And if they are substances, the second question is whether they are separate from 
sensible things, as the Platonists held, or exist in sensible things, as the Pythagoreans held. 

368. Now these questions are raised as problems which must be debated and settled below, 
because in these matters it is not only difficult to discover the truth, but it is not even easy to 
debate the matter adequately by finding probable arguments for either side of the question. 


LESSON 4 

Are All the Classes of Causes Studied by One Science or by Many? 
ARISTOTLE'S TEXT Chapter 2: 996a 18-996b 26 

190. Therefore let us discuss first the problem about which we first spoke (181): whether it is 
the office of one science or of many to study all the classes of causes. 

191. For how will it be the office of one science to come to principles since they are not 
contrary? 

192. Furthermore, in the case of many existing things not all the principles are present. For 
how can a principle of motion be present in all immobile things, or how can the nature of the 
good be found there? For everything which is a good in itself and by reason of its own nature 
is an end and thus a cause, because it is for its sake that other things come to be and exist. 
Further, the end and that for the sake of which something comes to be is the terminus of some 
action. But all actions involve motion. Therefore it would be impossible for this principle to 
be present in immobile things, nor could there be an autoagathon, i.e., a good in itself. Hence 
in mathematics too nothing is proved by means of this cause, nor is there any demonstration 
on the grounds that a thing is better or worse. Nor does anyone make any mention at all of 
anything of this kind. And for this reason some of the Sophists, for example, Aristippus, 
disregarded these. For in the other arts, even in the servile ones, such as building and 


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cobbling, all things are to be explained on the grounds that they are better or worse; but the 
mathematical sciences give no account of things which are good or evil. 

193. But on the other hand, if there are many sciences of the causes, and different sciences for 
different principles, which of these must be said to be the one that is being sought, or which 
one of those who have them is best informed about the subject under investigation? 

194. For it is possible for the same thing to have all the classes of causes; for example, in the 
case of a house the source of motion is the art and the builder, the reason for which is its 
function, the matter is earth and stones, and the form is the plan. 

195. Therefore, from the things which were established a little while ago (14-26:C 36-51) as 
to which of the sciences one should call wisdom, there is reason for calling every one of them 
such. For inasmuch as wisdom takes precedence and is a more authoritative science, and one 
which the others, like slaves, have no right to contradict, then the science which deals with 
the end and the good is such a science, because other things are for the sake of this. 

196. But insofar as wisdom has been defined (24:C 49) as the science of first causes and of 
what is most knowable, such a science will be about substance. For while a subject may be 
known in many ways, we say that he who knows what a thing is in its being knows it better 
than he who knows it in its nonbeing. And in the former case one knows better than another, 
especially he who knows what a thing is, and not how great it is or of what sort it is or 
anything that it is naturally disposed to do or to undergo. Further, in the case of other things 
too we think that we know every single thing, and those of which there are demonstrations, 
when we know what each is, for example, what squaring is, because it is finding the middle 
term. The same thing is true in other cases. 


197. But with regard to processes of generation and actions and every change, we think that 
we know these perfectly when we know the principle of motion. But this differs from and is 
opposite to the end of motion. And for this reason it seems to be the province of a different 
science to speculate about each one of these causes. 

COMMENTARY 

Q 1: Can one science consider many causes? 

369. Having raised the questions which cause difficulty in this science, Aristotle begins here 
to treat them dialectically. This is divided into three parts. In the first part, he treats the 
questions which pertain to the method of investigation of this science. In the second (403), he 
treats the questions which pertain to substances ("Furthermore, there is"). In the third (423), 
he treats the questions which pertain to the principles of substances ("Concerning the 
principles"). 

In regard to the first he does three things. First, he argues dialectically about this science's 
method of investigation, with reference to the causes by means of which it demonstrates; 
second (387), with reference to the first principles of demonstration ("But insofar"); and third 
(393), with reference to substances themselves ("And there is the problem"). 


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In regard to the first he does two things. First, he takes up again the question about which he 
plans to argue dialectically, concluding from the order in which the questions have been listed 
that it is necessary first to debate those issues which were stated first in the list of questions, 
namely, whether it is the function of one science or of many to investigate all the classes of 
causes; so that in this way the order of argument corresponds to the order in which the 
questions have been raised. 

370. For how will it be (191). 

Second, he gives the arguments relating to this question; and in regard to this he does three 
things. First (191), he gives an argument for the purpose of showing that it is not the office of 
a single science to consider all the classes of causes. Second (193:C 376), assuming that it 
belongs to different sciences to consider the different classes of causes, he asks which class of 
cause it is that is investigated by first philosophy. He argues on both sides of this question 
("But on the other hand"). Third (197:C 386), he draws from this second dispute the 
conclusion of the first arguments ("But-with regard to"). 

In regard to the first (191) he gives two arguments. He says that since it belongs to one 
science to consider contraries, how will it belong to one science to consider principles since 
they are not contrary? This view, if it is considered superficially, seems to be of no 
importance; for it appears to follow from the destruction of the antecedent, as if one were to 
argue thus: if principles are contraries, they belong to one science; therefore, if they are not 
contraries, they do not belong to one science. 

371. Therefore it can be said that in these disputes the Philosopher not only uses probable 
arguments but sometimes also uses sophistical ones when he gives arguments introduced by 
others. But it does not seem reasonable that in such an important matter so great a 
Philosopher would have introduced an argument which is both trifling and insignificant. 
Hence a different explanation must be given, namely, that if one rightly considers the nature 
of the various things which belong to the same science, some belong to a single 
science-insofar as they are different, but others insofar as they are reduced to some one thing. 
Hence many other different things are found to belong to one science insofar as they are 
reduced to one thing, for example, to one whole, one cause, or one subject. But contraries and 
all opposites belong essentially to one science by reason of the fact that one is the means of 
knowing the other. And from this comes this probable proposition that all different things 
which are contraries belong to one science. Therefore, if principles were different and were 
not contraries, it would follow that they would not belong to one science. 

372. Furthermore, in the case of (192). 

Here he gives the second argument, which runs thus. In the case of different things which 
belong to one science, whatever science considers one also considers another. This is evident 
in the case of contraries, which are different and belong essentially to one science without 
being reduced to some other unity. But not every science which considers one cause considers 
all causes. Therefore the study of all the causes does not belong to a single science. 

373. He proves the minor premise thus: Different sciences deal with different beings, and 
there are many beings to which all the causes cannot be assigned. He makes this dear, first, 
with regard to that cause which is called the source of motion; for it does not seem that there 
can be a principle of motion in immobile things. Now certain immobile things are posited, 
especially by the Platonists, who claim that numbers and substances are separate entities. 


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Hence, if any science considers these, it cannot consider the cause which is the source of 
motion. 

374. Second, he shows that the same thing is true of the final cause, which has the character 
of good. For it does not seem that the character of goodness can be found in immobile things, 
if it is conceded that everything which is good in itself and by reason of its own nature is an 
end. And it is a cause in the sense that all things come to be and exist because of it and for its 
sake. However, he says "everything which is good in itself and by reason of its own nature" 
in order to exclude the useful good, which is not predicated of the end but of the means to the 
end. Hence those things which are said to be good only in the sense that they are useful for 
something else arc not good in themselves and by reason of their own nature. For example, a 
bitter potion is not good in itself but only insofar as it is directed to the end, health, which is a 
good in itself. But an end, or that for the sake of which something comes to be, seems to be 
the terminus of an action. But all actions seem to involve motion. Therefore it seems to follow 
that this principle, i.e., the final cause, which has the character of goodness, cannot exist in 
immobile things. Further, since those things which exist of themselves apart from matter must 
be immobile, it therefore does not seem possible that "an autoagathon," i.e., a good-in-itself, 
exists, as Plato held. For he called all immaterial and unparticipated things entities which 
exist of themselves, just as he called the Idea of man, man-in-himself, as though not 
something participated in matter. Hence he also called the good-in-itself that which is its own 
goodness unparticipated, namely, the first principle of all things. 

375. Moreover, with a view to strengthening this argument he introduces an example. For, 
from the fact that there cannot be an end in the case of immobile things, it seems to follow 
that in the mathematical sciences, which abstract from matter and motion, nothing is proved 
by means of this cause, as in the science of nature, which deals with mobile things, something 
is proved by means of the notion of good. For example, we may give as the reason why man 
has hands that by them he is more capable of executing the things which reason conceives. 
But in the mathematical sciences no demonstration is made in this way, that something is so 
because it is better for it to be so, or worse if it were not so; as if one were to say, for 
example, that the angle in a semi-circle is a right angle because it is better that it should be so 
than be acute or obtuse. And because there can be, perhaps, another way of demonstrating by 
means of the final cause (for example, if one were to say that, if an, end is to be, then what 
exists for the sake of an end must first be), he therefore adds that in the mathematical sciences 
no one makes any mention at all of any of those things which pertain to the good or to the 
final cause. And for this reason certain sophists, as Aristippus, who belonged to the Epicurean 
school, completely disregarded any demonstrations which employ final causes, considering 
them to be worthless in view of the fact that in the servile or mechanical arts, for example, in 
the "art of building," i.e., in carpentry, and in that of "cobbling," all things are explained on 
the grounds that something is better or worse; whereas in the mathematical sciences, which 
are the noblest and most certain of the sciences, no mention is made of things good and evil. 

376. But on the other hand (193). 

Here he interjects another question. First, he states this question, which has two parts. The 
first part of the question is this. If different causes are considered by many sciences, so that a 
different science considers a different cause, then which of these sciences should be called the 
one "that is being sought," i.e., first philosophy? Is it the one which considers the formal 
cause, or the one which considers the final cause, or the one which considers one of the other 
causes? The second part of the question is this: If there are some things which have many 
causes, which one of those who consider those causes knows that subject best? 


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377. For it is possible (194). 

He clarifies the second part of the question by the fact that one and the same thing is found to 
have every type of cause. For example, in the case of a house the source of motion is the art 
and the builder; the reason, for which, or the final cause of the house, "is its function," i.e., its 
use, which is habitation; its material cause is the earth, from which the walls and floor are 
made; and its specifying or formal cause is the plan of the house, which the architect, after 
first conceiving it in his mind, gives to matter. 

378. Therefore from the things (195) 

Here he takes up again the question as to which of the aforesaid sciences we can call wisdom 
on the basis of the points previously established about wisdom at the beginning of this work 
(14:C 36), namely, whether it is the science which considers the formal cause, or the one 
which considers the final cause, or the one which considers one of the other causes. And he 
gives in order arguments relating to each of the three causes, saying that there seems to be 
some reason why "every oxie of the sciences," i.e., any one which proceeds by means of any 
cause at all, should be called by the name of wisdom. First, he speaks of that science which 
proceeds by means of the final cause. For it was stated at the beginning of this work that this 
science, which is called wisdom, is the most authoritative one, and the one which directs 
others as subordinates. Therefore, inasmuch as wisdom "takes precedence," i.e., is prior in the 
order of dignity and more influential in its authoritative direction of the other sciences 
(because it is not right that the others should contradict it but they should take their principles 
from it as its servants), it seems that that science "which deals with the end and the good," 
i.e., the one which proceeds by means of the final cause, is worthy of the name of wisdom. 
And this is true because everything else exists for the sake of the end, so that in a sense the 
end is the cause of all the other causes. Thus the science which proceeds by means of the final 
cause is the most important one. This is indicated by the fact that those arts which are 
concerned with ends are more important than and prior to the other arts; for example, the art 
of navigation is more important than and prior to the art of ship-building. Hence, if wisdom is 
pre-eminent and regulative of the other sciences, it seems that it proceeds especially by means 
of the final cause. 

379. But insofar as wisdom (196). 

Here he introduces the arguments relating to the formal cause. For it was said in the prologue 
of this work (26 :C 51) that wisdom is concerned with first causes and with whatever is most 
knowable and most certain. And according to this it seems to be concerned with "substance," 
i.e., it proceeds by means of the formal cause. For among the different ways of knowing 
things, we say that he who knows that something exists, knows more perfectly than he who 
knows that it does not exist. Hence in the Posterior Analytics the Philosopher proves that an 
affirmative demonstration is preferable to a negative demonstration. And among those who 
know something affirmatively, we say that one knows more perfectly than another. But we 
say that he knows more perfectly than any of the others who knows what a thing is, and not 
he who knows how great it is, or what it is like, or what it can do or undergo. Therefore, to 
know a thing itself in the most perfect way absolutely is to know what it is, and this is to 
know its substance. But even in knowing other things, for example, a thing's properties, we 
say that we know best every single thing about which there are demonstrations when we also 
know the whatness of their accidents and properties; because whatness is found not only in 
substance but also in accidents. 


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380. He gives the example of squaring, i.e., squaring a surface of equally distant sides which 
is not square but which we say we square when we find a square equal to it. But since every 
rectangular surface of equally distant sides is contained by the two lines which contain the 
right angle, so that the total surface is simply the product of the multiplication of one of these 
lines by the other, then we find a square equal to this surface when we find a line which is the 
proportional mean between these two lines. For example, if line A is to line B as line B is to 
line C, the square of line B is equal to the surface contained by C and A, as is proved in Book 
VI of Euclid's Elements. 

381. This becomes quite evident in the case of numbers. For 6 is the proportional mean 
between 9 and 4; for 9 is related to 6 in the ratio of 1 1/2 to 1, and so also is 6 to 4. Now the 
square of 6 is 36, which is also produced by multiplying 4 by 9; for 4 x 9 = 36. And it is 
similar in all other cases. 

382. But with regard to processes (197) 

Here he gives an argument pertaining to the cause of motion. For in processes of generation 
and actions and in every change we see that we may say that we know a thing when we know 
its principle of motion, and that motion is nothing else than the actuality of something mobile 
produced by a mover, as is stated in the Physics, Book III. He omits the material cause, 
however, because that cause is a principle of knowing in the most imperfect way; for the act 
of knowing is not caused by what is potential but by what is actual, as is stated below in Book 
IX (805 :C 1894) 

383. Then after having given those arguments which pertain to the second question, he 
introduces an argument which is based on the same reasons as were given above (191 :C 370 
ff.) in reference to the first question, namely, that it is the office of a different science to 
consider all these causes by reason of the fact that in different subject-matters different causes 
seem to have the principal role, for example, the source of motion in mobile things, the 
quiddity in demonstrable things, and the end in things which are directed to an end. 

384. However, we do not find that Aristotle explicitly solves this question later on, though his 
solution can be ascertained from the things which he establishes below in different places. For 
in Book IV (533) he establishes that this science considers being as being, and therefore that 

it also belongs to it, and not to the philosophy of nature, to consider first substances; for there 
are other substances besides mobile ones. 

But every substance is either a being of itself, granted that it is only a form; or it is a being by 
its form, granted that it is composed of matter and form. Hence inasmuch as this science 
considers being, it considers the formal cause before all the rest. But the first substances are 
not known by us in such a way that we know what they are, as can be understood in some 
way from the things established in Book IX (1904); and thus in our knowledge of them the 
formal cause has no place. 

But even though they are immobile in themselves, they are nevertheless the cause of motion 
in other things after the manner of an end. Hence inasmuch as this science considers first 
substances, it belongs to it especially to consider the final cause and also in a way the efficient 
cause. 

But to consider the material cause in itself does not belong to it in any way, because matter is 
not properly a cause of being but of some definite kind of being, namely, mobile substance. 


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However, such causes belong to the consideration of the particular sciences, unless perhaps 
they are considered by this science inasmuch as they are contained under being; for it extends 
its analysis to all things in this way. 

385. Now when these things are seen it is easy to answer the arguments which have been 
raised. For, first, nothing prevents the different causes in this science from belonging to a 
single existing thing, even though they are not contraries, because they are reducible to one 
thing — being in general — as has been stated (384). 

And in a similar way, even though not every science considers all of the causes, still nothing 
prevents one science from being able to consider all of the causes or several of them insofar 
as they are reducible to some one thing. But to be more specific, it must be said that in the 
case of immobile things nothing prevents the source of motion and the end or good from 
being investigated. By immobile things I mean here those which are still causes of motion, as 
the first substances. However, in the case of those things which are neither moved cause 
motion there is no investigation of the source of motion, or of the end in the sense of the end 
of motion, although an end can be considered as the goal of some operation which does not 
involve motion. For if there are held to be intellectual substances which do not cause motion, 
as the Platonists claimed, still insofar as they have an intellect and will it is necessary to hold 
that they have an end and a good which is the object of their will. However, the objects of 
mathematics neither are moved nor cause motion nor have a will. Hence in their case the 
good is not considered under the name of good and end, although in them we do consider 
what is good, namely, their being and what they are. Hence the statement that the good is not 
found in the objects of mathematics is false, as he proves below in Book IX (1888) . 

386. The reply to the second question is already clear; for a study of the three causes, about 
which he argued dialectically, belongs to this science. 


LESSON 5 

Are the Principles of Demonstration and Substance Considered by One Science or by Many? 
ARISTOTLE'S TEXT Chapter 2: 996b 26-997a 15 

198. But with respect to the principles of demonstration there is also the problem whether 
they are studied by one science or by many. By principles of demonstration I mean the 
common axioms from which fall] demonstrations proceed, e.g., "everything must either be 
affirmed or denied," and "it is impossible both to be and not to be at the same time," and all 
other such propositions. Is there one science which deals with these principles and with 
substance or are there different sciences? And, if not one, which of the two must be called the 
one that is now being sought? 

199. Now it would be unreasonable that these things should be studied by one science; for 
why should the study of these be proper to geometry rather than to any other science? In a 
similar way, then, if this study pertains to any science but cannot pertain to all, an 
understanding of these principles is no more proper to the science which studies substance 
than it is to any other science. 


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200. But at the same time how will there be a science of these principles? For we already 
know what each one of them is; and therefore the other arts use them as something known. 
However, if there is demonstration of them, there will have to be some subject-genus, and 
some of the principles will have to be properties and others axioms. For there cannot be 
demonstration of all things, since demonstration must proceed from something, and be about 
something, and [be demonstration] of certain things. It follows, then, that there is a single 
genus of demonstrable things; for all demonstrative sciences use axioms. 

201. But on the other hand, if the science which considers substance differs from the one 
which considers axioms, which of these sciences is the more important and prior one? For 
axioms are most universal and are the principles of all things. And if it does not belong to the 
philosopher to establish the truth and falsity [of these principles], to what other person will it 
belong? 

COMMENTARY 

Q. 2: Is the science of substance also that of first principles? 

387. Having debated the first question which had to do with the study of causes, Aristotle's 
intention here is to argue dialectically about the science which is concerned with the study of 
the first principles of demonstration; and in regard to this he does three things. First, he raises 
the question. Second (388), he argues one side of the question. Third (391), he argues on the 
other side of the question. 

Accordingly, he states, first, the problem relating to the first principles of demonstration, 
namely, whether the study of these principles belongs to one science or to many. Further, he 
explains what the principles of demonstration are, saying that they are the common 
conceptions of all men on which all demonstrations are based, i.e., inasmuch as the particular 
principles of the proper demonstrated conclusions derive their stability from these common 
principles. And he gives an example of first principles, especially this one, that everything 
must either be affirmed or denied [of some subject]. Another principle which he mentions is 
that it is impossible for the same thing both to be and not to be at the same time. Hence the 
question arises whether these principles and similar ones pertain to one science or to many. 
And if they pertain to one science, whether they pertain to the science which investigates 
substance or to another science. And if to another science, then which of these must be called 
wisdom, or first philosophy, which we now seek. 

388. Now it would be (199). 

Here he argues one side of the question with a view to showing that it is not the office of one 
science to consider all first principles, i.e. the first principles of demonstration and substance. 
He gives two arguments, of which the first runs thus: since all sciences employ these 
principles of demonstration, there seems to be no reason why the study of them should pertain 
to one science rather than to another; nor again does it seem reasonable that they should be 
studied by all sciences, because then it would follow that the same thing would be treated in 
different sciences; but that would be superfluous. Hence it seems to follow that no science 
considers these principles. Therefore, for the very same reason that it does not belong to any 
of the other sciences to give us a knowledge of such principles, for this reason too it follows 
that it does not belong to the science whose function it is to consider substance. 

389. But at the same time (200). 


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Here he gives the second argument, which runs thus. In the sciences there are two methods by 
which knowledge is acquired. One is that by which the whatness of each thing is known, and 
the other is that by which knowledge is acquired through demonstration. But it does not 
belong to any science to give us a knowledge of the principles of demonstration by means of 
the first method, because such knowledge of principles is assumed to be prior to all the 
sciences. For "we already know" what each one of them is, i.e., we know from the very 
beginning what these principles signify, and by knowing this the principles themselves are 
immediately known. And since such knowledge of principles belongs to us immediately, he 
concludes that all the arts and sciences which are concerned with other kinds of cognitions 
make use of these pinciples as things naturally known by us. 

390. But it is proved in the same way that a knowledge of these principles is not presented to 
us in any science by means of demonstration, because if there were demonstration of them, 
then three principles would have to be considered, namely, some subjectgenus, its properties 
and the axioms. In order to clarify this he adds that there cannot be demonstration of all 
things; for subjects are not demonstrated but properties are demonstrated of subjects. 
Concerning subjects, however, it is necessary to know beforehand whether they exist and 
what they are, as is stated in Book I of the Posterior Analytics. The reason is that 
demonstration must proceed from certain things as principles, which are the axioms, and be 
about something, which is the subject, and [be demonstration] of certain things, which are 
properties. Now according to this it is immediately evident of one of these three, i.e., the 
axioms, that they are not demonstrated, otherwise there would have to be certain axioms prior 
to the axioms; but this is impossible. Therefore, having dismissed this method of procedure as 
obvious, he proceeds to consider the subject-genus. For since one science has one 
subject-genus, then that science which would demonstrate axioms would have one 
subject-genus. Thus there would have to be one subjectgenus for all demonstrative sciences, 
because all demonstrative sciences use axioms of this kind. 

391. But on the other hand (201). 

Here he argues the other side of the question. For if it is said that there is one science which 
deals with sucn principles, and another which deals with substance, the problem will remain 
as to which of these sciences is the more important and prior one. For, on the one hand, since 
the axioms are most universal and are the principles of everything that is treated in any of the 
sciences, it seems that the science which deals with such principles is the most important one. 
Yet, on the other hand, since substance is the first and principal kind of being, it is evident 
that first-philosophy is the science of substance. And if it is not the same science which deals 
with substance and with the axioms, it will not be easy to state to which of the other sciences 
it belongs to consider the truth and falsity of these axioms, i.e., if it does not belong to first 
philosophy, which considers substance. 

392. The Philosopher answers this question in Book IV (590) of this work. He says that the 
study of the axioms belongs chiefly to the [first] philosopher inasmuch as it pertains to him to 
consider being in general, to which first principles of this kind essentially belong, as is most 
evident in the case of the very first principle: it is impossible for the same thing both to be and 
not to be [at the same time]. Hence all the particular sciences use principles of this kind just 
as they use being itself, although it is the first philosopher who is chiefly concerned with this. 
And the first argument is solved in this way. 

But the second argument is solved thus: the [first] philosopher does not consider principles of 
this kind in such a way as to make them known by defining them or by demonstrating them in 


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an absolute sense, but by refutation, i.e., by arguing disputatively against those who deny 
them, as is stated in Book IV (608). 


LESSON 6 

Are All Substances Considered by One Science or by Many? Does the Science of Substance 
Consider the Essential Accidents of Substance? 

ARISTOTLE'S TEXT Chapter 2: 997a 15-997a 34 

202. And there is the problem whether there is one science which deals with all substances, or 
many sciences. 

203. If there is not one science, then with what substances must this science deal? 

204. But it is unreasonable that there should be one science of all substances; for then one 
science would demonstrate all essential accidents, i.e., if it is true that every demonstrative 
science speculates about the essential accidents of some subject by proceeding from common 
opinions. Hence it is the office of the same science to study the essential accidents of the 
same subject-genus by proceeding from the same opinions. For it belongs to one science to 
consider that something is so, and it belongs to one science to consider the principles from 
which demonstrations proceed, whether to the same science or to a different one. Hence it 
belongs to one science to consider accidents, whether they are studied by these sciences or by 
one derived from them. 

205. Further, there is the problem whether this science is concerned only with substances or 
also with accidents. I mean, for example, that if a solid is a kind of substance, and also lines 
and surfaces, the question arises whether it is the function of the same science to know these 
and also the accidents of each class of things about which the mathematical sciences make 
demonstrations, or whether it is the concern of a different science. 

206. For if it is the concern of the same science, a particular one will undertake these 
demonstrations and this will be the one which deals with substance. However, there does not 
seem to be any demonstration of the quiddity. 

207. But if it is the concern of a different science, which science will it be that studies the 
accidents of substances? For to solve this is very difficult. 

COMMENTARY 

Qq. 3 & 6: Does the science of substance consider all substances as well as accidents? 

393. Having debated the questions the third question, which pertains to which pertain to the 
scope of investigation of this science, he now treats the study of substances and accidents. 
This is divided into two parts inasmuch as he discusses two questions on this point. The 
second (403) begins where he says, "Furthermore, there is." 


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In regard to the first he does three things. First, he raises the question whether there is one 
science that considers all substances, or whether there are many sciences that consider 
different substances. 

394. If there is not (203). 

Second, he argues the first side of the question with a view to showing that there is one 
science of all substances. For if there were not one science of all substances, then apparently 
it would be impossible to designate the substance which this science considers, because 
substance as substance is the primary kind of being. Hence it does not seem that one 
substance rather than another belongs to the consideration of the basic science. 

395. but it is unreasonable (204). 

Third, he argues the other side of the question, saying that it is unreasonable to hold that there 
is one science of all substances. For it would follow that there would be one demonstrative 
science of all essential accidents. And this is true because every science which demonstrates 
certain accidents speculates about the essential accidents of some particular subject, and it 
does this from certain common conceptions. Therefore, since a demonstrative science 
considers the accidents only of some particular subject, it follows that the study of some 
subject-genus belongs to the same science that is concerned with the study of the essential 
accidents of that genus and vice versa, so long as demonstrations proceed from the same 
principles. 

396. But sometimes it happens to be the function of some science to demonstrate from certain 
principles that a thing is so, and sometimes it happens to be the function of some science to 
demonstrate the principles from which it was demonstrated that a thing is so, sometimes to 
the same science and sometimes to a different one. 

An example of its being the function of the same science is seen in the case of geometry, 
which demonstrates that a triangle has three angles equal to two right angles in virtue of the 
principle that the exterior angle of a triangle is equal to the two interior angles opposite to it; 
for to demonstrate this belongs to geometry alone. And an example of its being the function 
of a different science is seen in the case of music, which proves that a tone is not divided into 
two equal semitones by reason of the fact that a ratio of 9 to 8, which is superparticular, 
cannot be divided into two equal parts. But to prove this does not pertain to the musician but 
to the arithmetician. It is evident, then, that sometimes sciences differ because their principles 
differ, so long as one science demonstrates the principles of another science by means of 
certain higher principles. 

397. But if it is assumed that the principles are identical, sciences could not differ so long as 
the accidents are the same and the subject-genus is the same, as if one science considered the 
subject and another its accidents. Hence it follows that that science which considers a 
substance will also consider its accidents, so that if there are many sciences which consider 
substances, there will be many sciences which consider accidents. But if there is only one 
science which considers substances, there will be only one science which considers accidents. 
But this is impossible, because it would then follow that there would be only one science, 
since there is no science which does not demonstrate the accidents of some subject. Therefore 
it is not the function of one science to consider all substances. 


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398. This is treated in Book IV (546) of this work, where it is shown that the examination of 
substance as substance belongs to the first science, whose province it is to consider being as 
being; and thus it considers all substances according to the common aspect of substance. 
Therefore it belongs to this science to consider the common accidents of substance. But it 
belongs to the particular sciences, which deal with particular substances, to consider the 
particular accidents of substances, just as it belongs to the science of nature to consider the 
accidents of mobile substance. However, among substances there is also a hierarchy, for the 
first substances are immaterial ones. Hence the study of them belongs properly to 
first-philosophy, just as the philosophy of nature would be first philosophy if there were no 
other substances prior to mobile corporeal substances, as is stated below in Book VI (1170). 

399. Further, there is the problem (205). 

Here he raises another question regarding the study of substance and accidents. Concerning 
this he does three things. First, he raises the question whether the investigation of this science 
is concerned with substance alone or also with the attributes that are accidents of substances. 
For example, if we say that lines, surfaces and solids are substances of some sort, as some 
held, the question arises whether it belongs to the same science to consider such things and 
also their proper accidents, which are demonstrated in the mathematical sciences, or whether 
it belongs to another science. 

400. For if it is the concern (206). 

Second, he argues one side of the question. For if it belongs to the same science to consider 
accidents and substances, then, since a science which considers accidents demonstrates 
accidents, it follows that a science which considers substance demonstrates substances. But 
this is impossible; for the definition of a substance, which expresses the quiddity' is 
indemonstrable. Hence it will belong to the same science to consider substances and 
accidents. 

401. But if it is the concern (207). 

Third, he argues the other side of the question: if different sciences consider substance and 
accident, it will not be possible to state which science it is that speculates about the accidents 
of substance; because the science which would do this would consider both, although this 
would seem to pertain to all sciences; for every science considers the essential accidents of its 
subject, as has been explained. 

402. The Philosopher answers this question in Book IV (570) of this work, saying that it is 
also the office of that science which is concerned with the study of substance and being to 
consider the proper accidents of substance and being. Yet it does not follow that it would 
consider each in the same way, i.e., by demonstrating substance as it demonstrates accidents, 
but by defining substance and by demonstrating that accidents either belong to or do not 
belong to it, as is explained more fully at the end of Book IX (1895) of this work. 


LESSON 7 


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Are There Certain Other Substances Separate from Sensible Things? Criticism of the 
Different Opinions Regarding the Objects of Mathematics 

ARISTOTLE'S TEXT Chapters 2 & 3: 997a 34-998a 21 

208. Furthermore, there is the problem whether sensible substances alone must be said to 
exist, or others besides these. And whether there is one genus or many genera of substances, 
as is held by those who speak of the Forms and the intermediate entities with which they say 
the mathematical sciences deal. 

209. Now the way in which we say that the Forms are both causes and substances in 
themselves has been treated in our first discussions concerning all of these things (69). 

210. But while they involve difficulty in many respects, it is no less absurd to say that there 
are certain other natures besides those which exist in the heavens, and that these are the same 
as sensible things, except that the former are eternal whereas the latter are corruptible. For 
they [i.e., the Platonists] say nothing more or less than that there is a man-in-himself and 
horse-in-itself and health-in-itself, which differ in no respect [from their sensible 
counterparts] ; in which they act like those who say that there are gods and that they are of 
human form. For just as the latter made nothing else than eternal men, in a similar way the 
former make the Forms nothing else than eternal sensible things. 

211. Furthermore, if anyone holds that there are intermediate entities in addition to the Forms 
and sensible substances, he will face many problems. For evidently there will be, in like 
manner, lines in addition to ordinary sensible lines, and the same will be true of other classes 
of things. Therefore, since astronomy is one of these [mathematical sciences], there will be a 
heaven in addition to the one we perceive, and a sun and moon, and the same will be true of 
the other celestial bodies. And how are we to accept these things? For it is unreasonable that a 
heaven should be immobile, but that it should be mobile is altogether impossible. The same 
thing is true of the things with which the science of perspective is concerned, and of 
harmonics in mathematics, because for the same reasons it is also impossible that these 
should exist apart from sensible things. For if there are intermediate sensible objects and 
senses, evidently there will be intermediate animals between animals-in-themselves and those 
which are corruptible. 

212. Again, one might also raise the question as to what things these sciences must 
investigate. For if geometry, which is the art of measuring the earth, differs from geodesy, 
which is the art of dividing the earth, only in this respect that the latter deals with things 
which are perceptible by the senses, whereas the former deals with those which are 
imperceptible, evidently there will be, in addition to the science of medicine, another science 
midway between the science of medicine itself and this particular science of medicine; and 
this will be true of the other sciences. But how is this possible? For then there will be certain 
healthy things besides those which are sensible and besides health-in-itself. 

213. Similarly, neither does it seem that geodesy is concerned with continuous quantities 
which are sensible and corruptible. For in this case it would be destroyed when they are 
destroyed. 

214. Nor again will astronomy deal with sensible continuous quantities, or with this heaven. 
For the lines we perceive by the senses are not such as those of which geometry speaks, since 
none of the things perceived by the senses are straight or round in this way. For the circle 


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does not touch the rule at a point, but in the way in which Protagoras spoke in arguing against 
the geometricians. Neither are the motions or revolutions of the heavens similar to the things 
of which geometry speaks, nor do points have the same nature as the stars. 

215. However, there are also some who say that these intermediate entities, which are below 
the Forms and above sensible things, do not exist outside of sensible things but in them. But 
to enumerate all the impossible consequences which follow from this theory would require 
too long a discussion. It will be sufficient to propose the following consideration. 

216. It is unreasonable that this should be so only in the case of such things, but evidently it is 
also possible for the Forms to exist in sensible things, because both of these views depend on 
the same argument. 

217. Furthermore, it would be necessary for two solids to occupy the same place. 

218. And [the objects of mathematics] would not be immobile since they exist in sensible 
things, which are moved. 

219. Moreover, on the whole, to what end would anyone hold that they exist but exist in 
sensible things? For the same absurdities as those described will apply to these suppositions. 
For there will be a heaven in addition to the one which we perceive, although it will not be 
separate but in the same place; but this is quite impossible. 

Chapter 3 

In these matters, then, it is difficult to see how it is possible to have any positive truth. 
COMMENTARY 

Q. 5: Are there substances besides sensible ones? 

403. Having debated the questions which pertain to the scope of this science, the Philosopher 
now treats dialectically the questions which pertain to the substances themselves with which 
this science is chiefly concerned. In regard to this he does three things. First, he raises the 
questions. Second (406), he indicates the source from which arguments can be drawn in 
support of one side of the question ("Now the way"). Third (407), he argues on the other side 
of the question ("But while they involve"). 

In regard to the first part of this division he raises two questions. The first question is whether 
sensible substances alone are found in the universe, as certain of the ancient philosophers of 
nature claimed, or whether besides sensible substances there are certain others, as the 
Platonists claimed. 

404. And assuming that besides sensible substances there are certain others, the second 
question is whether these substances belong to one genus, or whether there are many genera 
of substances. For he considers both opinions. For some thinkers held, that in addition to 
sensible substances there are only separate Forms, i.e., an immaterial man-in-himself and 
horse-in itself and so on for the other classes of things, whereas others held that there are 
certain other substances midway between the Forms and sensible things, namely, the objects 
of mathematics, with which they said the mathematical sciences deal. 


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405. The reason for this view is that they posited on the part of the intellect a twofold process 
of abstracting things: one whereby the intellect is said to abstract the universal from the 
particular, and according to this mode of abstraction they posited separate Forms, which 
subsist of themselves; and another [whereby the intellect is said to abstract] from sensible 
matter certain forms in whose definition sensible matter is not given, for example, the 
abstraction of circle from brass. And according to this mode of abstraction they posited 
separate objects of mathematics, which they said are midway between the Forms and sensible 
substances, because they have something in common with both: with the Forms inasmuch as 
they are separate from sensible matter, and with sensible substances inasmuch as many of 
them are found in one class, as many circles and many lines. 

406. Now the way in which (209). 

Then he shows how it is possible to argue one side of the question, saying that it has been 
stated "in our first discussions," i.e., in Book I (69:C 151), how the Forms are held to be both 
the causes of sensible things and substances which subsist of themselves. Hence, from the 
things which have been said there in presenting the views of Plato, arguments can be drawn in 
support of the affirmative side of the question. 

407. But while they involve (210). 

Here he advances reasons for the negative side. He does this, first (210), for the purpose of 
showing that the Forms are not separate from sensible things; and, second (211:C 410), for 
the purpose of showing that the objects of mathematics are not separate ("Furthermore, if 
anyone"). Now above in Book I (103:C 208) he gave many arguments against those who 
posited separate Forms; and, therefore, passing over those arguments, he gives the line of 
reasoning which seems most effective. He says (210) that while the position of those who 
posit separate Forms contains many difficulties, the position of those which is now given is 
no less absurd than any of the others, i.e., that someone should say that there are certain 
natures in addition to the sensible ones which are contained beneath the heavens. For the 
heavens constitute the limit of sensible bodies, as is proved in Book I of The Heavens and the 
World. But those who posited the Forms did not place them below the heavens or outside of 
it, as is stated in Book III of the Physics. Hence, in accordance with this he says that they 
posited certain other natures in addition to those which exist in the heavens. And they said 
that these opposite natures are the same as these sensible things both in kind and in their 
intelligible constitution, and that they exist in these sensible things; or rather they said that 
those natures are the Forms of these sensible things. For example, they said that a separate 
man constitutes the humanity of this particular man who is perceived by the senses, and that a 
man who is perceived by the senses is a man by participating in that separate man. Yet they 
held that these differ in this respect, that those immaterial natures are eternal, whereas these 
sensible natures are corruptible. 

408. That they hold those natures to be the same as these sensible things is clear from the fact 
that, just as man, horse, and health are found among sensible things, in a similar way they 
posited among these natures "a man-inhimself," i.e., one lacking sensible matter; and they did 
the same with regard to horse and health. Moreover, they claimed that nothing else existed in 
the class of separate substances except [the counterpart of] what existed materially in the 
sensible world. This position seems to be similar to that of those who held that the gods are of 
human form, which was the position of the Epicureans, as Tully states in The Nature of the 
Gods. For just as those who held that the gods are of human form did nothing else than make 
men eternal in nature, in a similar way those who claimed that there are Forms do nothing 


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else than hold that there are eternal sensible things, such as horse, ox, and the like. 

409. But it is altogether absurd that what is naturally corruptible should be specifically the 
same as what is naturally incorruptible; for it is rather the opposite that is true, namely, that 
corruptible and incorruptible things differ in kind to the greatest degree, as is said below in 
Book X (895:C 2137) Of this work. Yet it can happen that what is naturally corruptible is 
kept in being perpetually by Divine power. 

410. Furthermore, if anyone (211). 

Then he argues against those who claimed that the objects of mathematics are midway 
between the Forms and sensible things. First (211:C 410), he argues against those who held 
that the objects of mathematics are intermediate entities and are separate from sensible things; 
and, second (215:C 417), against those who held that the objects of mathematics exist but 
exist in sensible things ("However, there are"). 

In regard to the first he does two things. First, he introduces arguments against the first 
position. Second (214:C 416), he argues in support of this position ("Nor again"). 

He brings up three arguments against the first position. The first argument is this: just as there 
is a mathematical science about the line, in a similar way there are certain mathematical 
sciences about other subjects. If, then, there are certain lines in addition to the sensible ones 
with which geometry deals, by the same token there will be, in all other classes of things with 
which the other mathematical sciences deal, certain things in addition to those perceived by 
the senses. But he shows that it is impossible to hold this with regard to two of the 
mathematical sciences. 

411. He does this, first, in the case of astronomy, which is one of the mathematical sciences 
and which has as its subject the heavens and the celestial bodies. Hence, according to what 
has been said, it follows that there is another heaven besides the one perceived by the senses, 
and similarly another sun and another moon, and so on for the other celestial bodies. But this 
is incredible, because that other heaven would be either mobile or immobile. If it were 
immobile, this would seem to be unreasonable, since we see that it is natural for the heavens 
to be always in motion. Hence the astronomer also makes some study of the motions of the 
heavens. But to say that a heaven should be both separate and mobile is impossible, because 
nothing separate from matter can be mobile. 

412. Then he shows that the same view is unacceptable in the case of other mathematical 
sciences, for example, in that of perspective, which considers visible lines, and "in the case of 
harmonics," i.e., in that of music, which studies the ratios of audible sounds. Now it is 
impossible that there should be intermediate entities between the Forms and sensible things; 
because, if these sensible things — sounds and visible lines — were intermediate entities, it 
would also follow that there are intermediate senses. And since senses exist only in an animal, 
it would follow that there are also intermediate animals between the Form animal, and 
corruptible animals; but this is altogether absurd. 

413. Again, one might (212). 

The second argument [which he uses against the possibility of the objects of mathematics 
being an intermediate class of entities separate from sensible things] is as follows. If in those 
classes of things with which the mathematical sciences deal there are three classes of 


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things — sensible substances, Forms and intermediate entities, then since the intelligible 
structure of all sensible things and of all Forms seems to be the same, it appears to follow that 
there are intermediate entities between any sensible things at all and their Forms. Hence there 
remains the problem as to what classes of things are included in the scope of the mathematical 
sciences. For if a mathematical science such as geometry differs from geodesy, which is the 
science of sensible measurements, only in this respect that geodesy deals with sensible 
measurements, whereas geometry deals with intermediate things which are not sensible, there 
will be in addition to all the sciences which consider sensible things certain [other] 
mathematical sciences which deal with these intermediate entities. For example, if the science 
of medicine deals with certain sensible bodies, there will be in addition to the science of 
medicine, and any like science, some other science which will be intermediate between the 
science of medicine which deals with sensible bodies and the science of medicine which deals 
with the Forms. But this is impossible; for since medicine is about "healthy things," i.e., 
things which are conducive to health, then it will also follow, if there is an intermediate 
science of medicine, that there will be intermediate health-giving things in addition to the 
health-giving things perceived by the senses and absolute health, i.e., health-in-itself, which is 
the Form of health separate from matter. But this is clearly false. Hence it follows that these 
mathematical sciences do not deal with certain things which are intermediate between 
sensible things and the separate Forms. 

414. Similarly, neither (213). 

Then he gives the third argument [against the possibility of the objects of mathematics being 
an intermediate class] ; and in this argument one of the points in the foregoing position is 
destroyed, namely, that there would be a science of continuous quantities which are 
perceptible; and thus, if there were another science of continuous quantities, it would follow 
from this that there would be intermediate continuous quantities. Hence he says that it is not 
true that geodesy is a science of perceptible continuous quantities, because such continuous 
quantities are corruptible. It would follow, then, that geodesy is concerned with corruptible 
continuous quantities. But it seems that a science is destroyed when the things with which it 
deals are destroyed; for when Socrates is not sitting, our present knowledge that he is sitting 
will not be true. Therefore it would follow that geodesy, or geosophics as other readings say, 
is destroyed when sensible continuous quantities are destroyed; but this is contrary to the 
character of science, which is necessary and incorruptible. 

415. Yet this argument can be brought in on the opposite side of the question inasmuch as one 
may say that he intends to prove by this argument that there are no sciences of sensible things, 
so that all sciences must be concerned with either the intermediate entities or the Forms. 

416. Nor again will (214) 

Here he argues in support of this position, as follows: it belongs to the very notion of science 
that it should be concerned with what is true. But this would not be the case unless it were 
about things as they are. Therefore the things about which there are sciences must be the same 
in themselves as they are shown to be in the sciences. But perceptible lines are not such as 
geometry says they are. He proves this on the grounds that geometry demonstrates that a 
circle touches "the rule," i.e., a straight line, only at a point, as is shown in Book III of 
Euclid's Elements. But this is found to be true of a circle and a line in the case of sensible 
things. Protagoras used this argument when he destroyed the certainties of the sciences 
against the geometricians. Similarly, the movements and revolutions of the heavens are not 
such as the astronomers describe them; for it seems to be contrary to nature to explain the 


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movements of the celestial bodies by means of eccentrics and epicycles and other different 
movements which the astronomers describe in the heavens. Similarly, neither are the 
quantities of the celestial bodies such as the astronomers describe them to be, for they use 
stars as points even though they are still bodies having extension. It seems, then, that 
geometry does not deal with perceptible continuous quantities, and that astronomy does not 
deal with the heaven which we perceive. Hence it remains that these sciences are concerned 
with certain other things, which arc intermediate. 

417. However, there are (215) 

Here he argues against another position. First, he states the point at issue. Second (216:C 
418), he brings in arguments germane to his purpose ("It is unreasonable"). 

Accordingly, he says, first (215), that some thinkers posit natures midway between the Forms 
and sensible things, yet they do not say that these natures are separate from sensible things 
but exist in sensible things themselves. This is clear regarding the opinion of those who held 
that there are certain self-subsistent dimensions which penetrate all sensible bodies, which 
some thinkers identify with the place of sensible bodies, as is stated in Book IV of the Physics 
and is disproved there. Hence he says here that to pursue all the absurd consequences of this 
position is a major undertaking, but that it is now sufficient to touch on some points briefly. 

418. It is unreasonable (216). 

Then he brings four arguments against this position. The first runs as follows. It seems to be 
for the same reason that in addition to sensible things the Forms and objects of mathematics 
are posited, because both are held by reason of abstraction on the part of the intellect. If, then, 
the objects of mathematics are held to exist in sensible things, it is fitting that not only they 
but also the Forms themselves should exist there. But this is contrary to the opinion of those 
who posit [the existence of] the Forms. For they hold that these are separate, and not that they 
exist anywhere in particular. 

419. Furthermore, it would be (217) 

Here he gives the second argument, which runs thus: if the objects of mathematics differ from 
sensible things yet exist in them, since a body is an object of mathematics, it follows that a 
mathematical body exists simultaneously with a sensible body in the same subject. Therefore 
"two solids," i.e., two bodies, will exist in the same place. This is impossible not only for two 
sensible bodies but also for a sensible body and a mathematical one, because each has 
dimensions, by reason of which two bodies are prevented from being in the same place. 

420. Furthermore, if anyone (211). 

Then he argues against those who claimed that the objects of mathematics are midway 
between the Forms and sensible things. First (211:C 410), he argues against those who held 
that the objects of mathematics are intermediate entities and are separate from sensible things; 
and, second (215:C 417), against those who held that the objects of mathematics exist but 
exist in sensible things ("However, there are"). 

In regard to the first he does two things. First, he introduces arguments against the first 
position. Second (214:C 416), he argues in support of this position ("Nor again"). 


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He brings up three arguments against the first position. The first argument is this: just as there 
is a mathematical science about the line, in a similar way there are certain mathematical 
sciences about other subjects. If, then, there are certain lines in addition to the sensible ones 
with which geometry deals, by the same token there will be, in all other classes of things with 
which the other mathematical sciences deal, certain things in addition to those perceived by 
the senses. But he shows that it is impossible to hold this with regard to two of the 
mathematical sciences. 

421. He does this, first, in the case of astronomy, which is one of the mathematical sciences 
and which has as its subject the heavens and the celestial bodies. Hence, according to what 
has been said, it follows that there is another heaven besides the one perceived by the senses, 
and similarly another sun and another moon, and so on for the other celestial bodies. But this 
is incredible, because that other heaven would be either mobile or immobile. If it were 
immobile, this would seem to be unreasonable, since we see that it is natural for the heavens 
to be always in motion. Hence the astronomer also makes some study of the motions of the 
heavens. But to say that a 

422. Now the Philosopher treats these questions below in Books XII, XIII and XIV of this 
work, where he shows that there are neither separate mathematical substances nor Forms. The 
reasoning which moved those who posited the objects of mathematics and the Forms, which 
are derived from an abstraction of the intellect, is given at the beginning of Book XIII. For 
nothing prevents a thing which has some particular attribute from being considered by the 
intellect without its being viewed under this aspect and yet be considered truly, just as a white 
man can be considered without white being considered. Thus the intellect can consider 
sensible things not inasmuch as they are mobile and material but inasmuch as they are 
substances or continuous quantities; and this is to abstract the thing known from matter and 
motion. However, so far as the thing known is concerned, the intellect does not abstract in 
such a way that it understands continuous quantities and forms to exist without matter and 
motion. For then it would follow either that the intellect of the one abstracting is false, or that 
the things which the intellect abstracts are separate in reality. 


LESSON 8 

Are Genera Principles of Things? And If So, Does This Apply to The Most Universal Genera 
or to Those Nearest to Individuals? 

ARISTOTLE'S TEXT Chapter 3: 998a 20-999a 23 

220. Concerning the principles of things there is the problem whether genera must be 
regarded as the elements and principles of things, or rather the first things of which each thing 
is composed inasmuch as they are intrinsic. 

221. just as the elements and principles of a word seem to be those things of which all words 
are first composed, but not word in common. And just as we say that the elements of 
diagrams are those things whose demonstrations are found in the demonstrations of others, 
either of all or of most of them. 


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222. Furthermore, those who say that the elements of bodies are many, and those who say that 
they are one, call the things of which bodies are composed and constituted their principles, as 
Empedocles says that fire and water and those things which are included with these are the 
elements from which existing things derive their being; but he does not speak of them as the 
genera of existing things. 

223. And again if anyone wished to speculate about the nature of other things, in finding out 
in regard to each (a bed, for example) of what parts it is made and how it is put together, he 
will come to know its nature. And according to these arguments genera are not the principles 
of existing things. 

224. But if we know each thing through definitions, and genera are the principles of 
definitions, genera must be the principles of the things defined. 

225. And if in order to acquire scientific knowledge of existing things it is necessary to 
acquire scientific knowledge of their species, according to which they are said to be beings, 
then genera are the principles of species. 

226. Moreover, some of those who say that the elements of existing things are the one or 
being or the great and small, seem to use these as genera. 

227. But it is not possible to speak of principles in both ways; for the meaning of substance is 
one. Therefore a definition by means of genera will differ from one which gives the intrinsic 
constituents. 

228. Again, if genera are the principles of things in the fullest sense, there is the question 
whether the first genera must be thought to be principles, or those which are lowest and are 
predicated of individual things. For this also raises a problem. 

229. For if universals are the principles of things to a greater degree, evidently these must be 
the highest genera, because it is most properly these which are predicated of all existing 
things. Therefore there will be as many principles of existing things as there are first genera. 
Hence being and unity will be principles and substances, for it is these especially which are 
predicated of all existing things. 

It is impossible, however, that unity or being should be a single genus of existing things; for it 
is necessary both that the differences of each genus exist and that each be one. But it is 
impossible either that species be predicated of the differences of their own genera, or that a 
genus be so predicated independently of its species. If, then, unity or being is a genus, no 
difference will be one and a being. But if unity and being are not genera, neither will they be 
principles, supposing that genera are principles. 

230. Further, those things which are intermediate and are taken along with differences will be 
genera down to individuals. But some seem to be such, whereas others do not. Again, 
differences are principles to a greater degree than genera; and if they are principles, principles 
will be infinite in number, so to speak. And [this will appear] in another way also if one holds 
that the first genus is a principle. 

231. But, on the other hand, if unity is a specific principle to a greater degree, and unity is 
indivisible, and everything indivisible is such either in quantity or in species, and what is 
indivisible in species is prior, and genera are divisible into species, then it will be rather the 


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lowest predicate which is one. For man is not the genus of particular men. 

232. Further, in the case of those things to which prior and subsequent apply, it is not possible 
in their case that there should be something which exists apart from them. For example, if the 
number two is the first of numbers, there will not be any number apart from the species of 
numbers; nor, likewise, any figure apart from the species of figures. But if the genera of these 
things do not [exist apart from the species], then in the case of other things the teaching will 
be that there are genera apart from the species; for of these things there seem especially to be 
genera. But among individual things one is not prior and another subsequent. 

233. Further, where one thing is better and another worse, that which is better is always prior; 
so that there will be no genus of these things. From these considerations, then, it seems that it 
is the terms predicated of individuals, rather than genera, which are principles. 

234. But again it is not easy to state how one must conceive these to be the principles of 
things. .For a principle or cause must be distinct from the things of which it is the principle or 
cause, and must be able to exist apart from them. But why should one think that anything 
such as this exists apart from singular things, except that it is predicated universally and of all 
things? But if this is the reason, then the more universal things are, the more they must be 
held to be principles. Hence the first genera will be principles of things. 

COMMENTARY 

Q. 9: What is the difference between genera and elements? 

423. Having debated the questions which were raised about substances, the Philosopher now 
treats dialectically the questions which were raised about principles. This is divided into two 
parts. In the first he discusses the questions which asked what the principles of things are; and 
in the second (456), the questions which asked what kind of things the principles are ("Again, 
there is the problem"). 

In the first part of this division he discusses two questions: first, whether universals are the 
principles of things; and second (443), whether any principles are separate from matter ("But 
there is a problem"). 

In regard to the first he discusses two questions, of which the first is whether genera are the 
principles of things. The second (431) asks which genera these are, whether the first genera or 
the others ("Again, if genera"). 

In regard to the first he does two things: first, he raises the question; and second (424), he 
treats it dialectically ("Just as the elements"). 

The first question has to do with the principles of things: whether it is necessary to accept or 
believe that those genera which are predicated of many things are the elements and principles 
of things, or rather that those parts of which every single thing is composed must be called the 
elements and principles of things. But he adds two conditions, one of which is "inasmuch as 
they are intrinsic," which is given in order to distinguish these parts from a contrary and a 
privation. For white is said to come from black, or the non-white, although these are not 
intrinsic to white. Hence they are not its elements. The other condition is what he calls "the 
first things," which is given in order to distinguish them from secondary components. For the 
bodies of animals are composed of flesh and nerves, which exist within the animal; yet these 


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are not called the elements of animals, because they are not the first things of which an animal 
is composed, but rather fire, air, water and earth, from which flesh and nerves derive their 
being. 

424. Just as the elements (221). 

Here he treats this question dialectically; and in regard to this he does three things. First, he 
shows that the first things of which anything is composed are its principles and elements. 
Second (224:C 427), he argues the opposite side of the question ("But if we know"). Third 
(227:C 430), he rejects one answer by which it could be said that both of these [i.e., genera 
and constituent parts] are the principles and elements of things ("But it is not"). 

In regard to the first he gives three arguments. The first of these proceeds from natural 
phenomena, in which he makes his thesis evident by two examples. The first example which 
he gives if that of a word, whose principle and element is not said to be the common term 
word but rather the first constituents of which all words are composed, which are called 
letters. He gives as a second example, diagrams, i.e., the demonstrative descriptions of 
geometrical figures. For the elements of these diagrams are not said to be the common term 
diagram but rather those theorems whose demonstrations are found in the demonstrations of 
other geometrical theorems, either of all or of most of them, because the other demonstrations 
proceed from the supposition of the first demonstrations. Hence the book of Euclid is called 
The Book of Elements, because the first theorems of geometry, from which the other 
demonstrations proceed, are demonstrated therein. 

425. Furthermore, those who (222). 

Here he gives the second argument which also employs certain examples drawn from nature. 
He says that those who hold that the elements of bodies are either one or many, say that the 
principles and elements of bodies are those things of which bodies are composed and made up 
as intrinsic constituents. Thus Empedocles says- that the elements of natural bodies are fire 
and water and other things of this kind, which along with these he calls the elements of 
things; and natural bodies are constituted of these first things inasmuch as they are intrinsic. 
Moreover, they [i.e., the philosophers of nature] held that in addition to these two principles 
there are four others — air, earth, strife and friendship — as was stated in Book I (50:C 104). 
But neither Empedocles nor the other philosophers of nature said that the genera of things are 
the principles and elements of these natural bodies. 

426. And again if anyone (223). 

Here he gives the third argument, which involves things made by art. He says that if someone 
wished to "speculate about their nature," i.e., about the definition which indicates the essence 
of other bodies than natural ones, namely, of bodies made by human art, for example, if one 
wished to know a bed, it would be necessary to consider of what parts it is made and how 
they are put together; and in this way he would know the nature of a bed. And after this he 
concludes that genera are not the principles of existing things. 

427. But if we know (224). 

Here he argues the other side of the question. He gives three arguments, the first of which is 
as follows. Each thing is known through its definition. Therefore, if a principle of being is the 
same as a principle of knowing, it seems that anything which is a principle of definition is 


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also a principle of the thing defined. But genera are principles of definitions, because 
definitions are first composed of them. Hence genera are the principles of the things defined. 

428. And if in order to (225) 

Here he gives the second argument, which runs thus. Scientific knowledge of each thing is 
acquired by knowing the species from which it gets its being, for Socrates can be known only 
by understanding that he is man. But genera are principles of species, because the species of 
things are composed of genera and differences. Therefore genera are the principles of existing 
things. 

429. Moreover, some of those (226). 

Here he gives a third argument, which is based on the authority of the Platonists, who held 
that the one and being are the principles of things, and also the great and small, which are 
used as genera. Therefore genera are the principles of things. 

430. But it is not possible (227) 

Here he excludes one answer which would say that both of these are principles. He says that it 
is impossible to say that both of these are "principles," i.e., both the elements, or the parts of 
which something is composed, and genera. He proves this by the following argument. Of 
each thing there is one definite concept which exposes its substance, just as there is also one 
substance of each thing. But the definitive concept which involves genera is not the same as 
the one which involves the parts of which a thing is composed. Hence it cannot be true that 
each definition indicates a thing's substance. But the definitive concept which indicates a 
thing's substance cannot be taken from its principles. Therefore it is impossible that both 
genera and the parts of which things are composed should be simultaneously and being 
cannot be genera of all the principles of things. 

431. Again, if genera (228). 

Then he treats the second question dialectically. First, he raises the question; and second 
(432), he brings up arguments relative to this question ("For if universals"). 

Accordingly, he says that if we hold that genera are the principles of things in the fullest sense 
which of these genera should be considered to be the principles of things to a greater degree? 
Must we consider those "genera" which are first in number, namely, the most common, or 
also the lowest genera, which are proximately predicated of the individual, i.e., the lowest 
species. For this is open to question, as is clear from what follows. 

432. For if universals (229). 

Here he argues about the question which was proposed; and in regard to this he does three 
things. First, he introduces arguments to show that the first genera cannot be principles. 
Second (231:C 436), he introduces arguments to show that the last species should rather be 
called the principles of things ("But, on the other hand"). Third (234:C 441), he debates the 
proposed question ("But again it is"). 

In regard to the first (229) he gives three arguments, of which the first runs thus: if genera are 
principles to the extent that they are more universal, then those which are most universal, i.e., 


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those which are predicated of all things, must be the first genera and the principles of things 
in the highest degree. Hence there will be as many principles of things as there are most 
common genera of this kind. But the most common of all genera are unity and being, which 
are predicated of all things. Therefore unity and being will be the principles and substances of 
all things. But this is impossible, because unity and being cannot be genera of all things. For, 
since unity and being are most universal, if they were principles of genera, it would follow 
that genera would not be the principles of things. Hence the position which maintains that the 
most common genera are principles is an impossible one, because from it there follows the 
opposite of what was held, namely, that genera are not principles. 

433. That being and unity cannot be genera he proves by this argument: since a difference 
added to a genus constitutes a species, a species cannot be predicated of a difference without 
a genus, or a genus without a species. That it is impossible to predicate a species of a 
difference is clear for two reasons. First, because a difference applies to more things than a 
species, as Porphyry says; ' and second, because, since a difference is given in the definition 
of a species, a species can be predicated essentially of a difference only if a difference is 
understood to be the subject of a species, as number is the subject of evenness in whose 
definition it is given. This, however, is not the case; but a difference is rather a formal 
principle of a species. Therefore a species cannot be predicated of a difference except, 
perhaps, in an incidental way. Similarly too neither can a genus, taken in itself, be predicated 
of a difference by essential predication. For a genus is not given in the definition of a 
difference, because a difference does not share in a genus, as is stated in Book IV of The 
Topics; nor again is a difference given in the definition of a genus. Therefore a genus is not 
predicated essentially of a difference in any way. Yet it is predicated of that which "has a 
difference," i.e., of a species, which actually contains a difference. Hence he says that a 
species is not predicated of the proper differences of a genus, nor is a genus independently of 
its species, because a genus is predicated of its differences inasmuch as they inhere in a 
species. But no difference can be conceived of which unity and being are not predicated, 
because any difference of any genus is a one and a being, otherwise it could not constitute any 
one species of being. It is impossible, then, that unity and being should be genera. 

434. Further, those things (230) 

Then he gives the second argument, which runs thus: if genera are called principles because 
they are common and predicated of many things, then for a like reason all those things which 
are principles because they are common and predicated of many will have to be genera. But 
all things which are intermediate between the first genera and individuals, namely, those 
which are considered together with some differences, are common predicates of many things. 
Hence they are both principles and genera. But this is evidently false. For some of them are 
genera, as subaltern species, whereas others are not, as the lowest species. It is not true, then, 
that the first or common genera are the principles of things. 

435. Further, if the first genera are principles, because they are the principles by which we 
know species, then differences will be principles to a greater degree, because differences are 
the formal principles of species; and form or actuality is chiefly the principle of knowing. But 
it is unfitting that differences should be the principles of things, because in that case there 
would be an infinite number of principles, so to speak; for the differences of things are 
infinite, so to speak; not infinite in reality but to us. That they are infinite in number is 
revealed in two ways: in one way if we consider the multitude of differences in themselves; in 
another way if we consider the first genus as a first principle, for evidently innumerable 
differences are contained under it. The first genera, then, are not the principles of things. 


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436. But on the other hand (231). 

Then he shows that the lowest species are principles to a greater degree than genera. He gives 
three arguments, of which the first runs thus: according to the Platonists it is the one which 
seems to have "the nature," 3 or character, of a principle to the greatest degree. Indeed, unity 
has the character of indivisibility, because a one is merely an undivided being. But a thing is 
indivisible in two ways, namely, in quantity and in species: in quantity, as the point and unit, 
and this is a sort of indivisibility opposed to the division of quantity; and in species, as what is 
not divided into many species. But of these two types of indivisibility the first and more 
important one is indivisibility in species, just as the species of a thing is prior to its quantity. 
Therefore that which is indivisible in species is more of a principle because it is indivisible in 
quantity. And in the division of quantity the genus seems to be more indivisible, because 
there is one genus of many species; but in the division of species one species is more 
indivisible. Hence the last term which is predicated of many, which is not a genus of many 
species, namely, the lowest species, is one to a greater degree in species than a genus; for 
example, man or any other lowest species is not the genus of particular men. Therefore a 
species is a principle to a greater degree than a genus. 

437. Further, in the case of (232). 

Then he gives the second argument, which is based on a certain position of Plato; for at one 
time Plato held that there is some one thing which is predicated of many things without 
priority and posteriority, and that this is a separate unity, as man is separate from all men; and 
at another time he held that there is some one thing which is predicated of many things 
according to priority and posteriority, and that this is not a separate unity. This is what 
Aristotle means when he says "in the case of those things to which prior and subsequent 
apply," i.e., that when one of the things of which a common term is predicated is prior to 
another, it is impossible in such cases that there should be anything separate from the many 
things of which this common term is predicated. For example, if numbers stand in such a 
sequence that two is the first species of number, no separate Idea of number will be found to 
exist apart from all species of numbers. And on the same grounds no separate figure will be 
found to exist apart from all species of figures. 

438. The reason for this can be that a common attribute is held to be separate so as to be some 
first entity in which all other things participate. If, then, this first entity is a one applicable to 
many in which all other things participate, it is not necessary to hold that there is some 
separate entity in which all things participate. But all genera seem to be things of this kind, 
because all types of genera are found to differ insofar as they are more or less perfect, and 
thus insofar as they are prior and subsequent in nature. Hence, if in those cases in which one 
thing is prior to another it is impossible to regard anything common as a separate entity, on 
the supposition that there is a genus apart from species, then "in the case of other things the 
teaching" will [differ], i.e., there will be another doctrine and rule concerning them, and the 
foregoing rule will not apply to them. But considering the individuals of one species, it is 
evident that one of these is not prior and another subsequent in nature but only in time. And 
thus according to Plato's teaching a species is separate. Since, then, these common things are 
principles inasmuch as they are separate, it follows that a species is a principle to a greater 
degree than a genus. 

439. Further, where one thing (233) 


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Here he gives the third argument, which makes use of the notions "better or worse." For in all 
those cases where one thing is better than another, that which is better is always prior in 
nature. But there cannot be held to be one common genus of those things which exist in this 
way. Hence there cannot be held to be one separate genus in the case of those things in which 
one is better and another worse; and thus the conclusion is the same as the above. For this 
argument is introduced to strengthen the preceding one, so to speak, i.e., with a view to 
showing that there is priority and posteriority among the species of any genus. 

440. And from these three arguments he draws the conclusion in which he is chiefly 
interested, namely, that the lowest species, which are predicated immediately of individuals, 
seem to be the principles of things to a greater degree than genera. 

441. But again it is not (234). 

Here he argues the opposite side of the question, as follows: a principle and a cause are 
distinct from the things of which they are the principle and cause, and are capable of existing 
apart from them. And this is true, because nothing is its own cause. He is speaking here of 
extrinsic principles and causes, which are causes of a thing in its entirety. But the only thing 
that is held to exist apart from singular things is what is commonly and universally predicated 
of all things. Therefore the more universal a thing is, the more separate it is, and the more it 
should be held to be a principle. But the first genera are most universal. Therefore the first 
genera are the principles of things in the highest degree. 

442. Now the solution to these questions is implied in this last argument. For according to this 
argument genera or species are held to be universal principles inasmuch as they are held to be 
separate. But the fact that they are not separate and self-subsistent is shown in Book VII 
(1592) of this work. Hence the Commentator also shows, in Book VIII, that the principles of 
things are matter and form, to which genus and species bear some likeness. For a genus is 
derived from matter and difference from form, as will be shown in the same book (720). 
Hence, since form is more of a principle than matter, species will consequently be principles 
more than genera. But the objection which is raised against this, on the grounds that genera 
are the principles of knowing a species and its definitions, is answered in the same way the 
objection raised about their separateness. For, since a genus is understood separately by the 
mind without understanding its species, it is a principle of knowing. And in the same way it 
would be a principle of being, supposing that it had a separate being. 


LESSON 9 

Do Any Universals Exist Apart from the Singular Things Perceived by the Senses and from 
Those Which Are Composed of Matter and Form? 

ARISTOTLE'S TEXT Chapter 4: 999a 24-999b 20 

235. But there is a problem connected with these things, which is the most difficult of all and 
the most necessary to consider, with which our analysis is now concerned. 

236. For if there is nothing apart from singular things, and singular things are infinite in 
number, how is it possible to acquire scientific knowledge of them? For insofar as there is 


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something that is one and the same, and insofar as there is something universal [which relates 
to singular things], to that extent we acquire knowledge of them. 

237. But if this is necessary, and there must be something apart from singular things, it will be 
necessary that genera exist apart from singular things, and they will be either the last or the 
first. But the impossibility of this has already appeared from our discussion. 

238. Further, if there is something apart from the concrete whole (which is most disputable), 
as when something is predicated of matter, if there is such a thing, the problem arises whether 
it must exist apart from all concrete wholes, or apart from some and not from others, or apart 
from none. 

239. If, then, there is nothing apart from singular things, nothing will be intelligible, but all 
things will be sensible, and there will be no science of anything, unless one might say that 
sensory perception is science. 

240. Further, neither will anything be eternal or immobile; for all sensible things perish and 
are subject to motion. 

241. But if there is nothing eternal, neither can there be generation; for there must be 
something which has come to be and something from which it comes to be; and the last of 
these must be ungenerated, since the process of generation must have a limit, and since it is 
impossible for anything to come to be from non-being. 

242. Further, since generation and motion exist, there must be a terminus; for no motion is 
infinite but every motion has a terminus. And that which is incapable of coming to be cannot 
be generated. But that which has come to be must exist as soon as it has come to be. 

243. Further, if matter exists because it is ungenerated, it is much more reasonable that 
substance should exist, since that is what it (matter) eventually comes to be. For if neither the 
one nor the other exists, nothing at all will exist. But if this is impossible, there must be 
something besides the synolon, and this is the form or specifying principle. 

COMMENTARY 

Q. 10: Is there anything separate from sensible things, which is their principle? 

443. Having debated the question whether universals are the principles of things, the 
Philosopher now raises a question about their separability, namely, whether there is anything 
separate from sensible things as their principle. In regard to this he considers two questions. 
The first (443) Of these is whether universals are separate from singular things. The second 
(447) is whether there is any formal [principle] separate from things which are composed of 
matter and form ("Further, if there is something"). 

In regard to the first he does three things. First, he describes the problem. Second (444), he 
argues one side of the question ("For if there is nothing"). Third (445), he argues the other 
side of the question ("But if this is"). 

Accordingly, this problem arises with regard to a point mentioned in the last argument of the 
preceding question, namely, whether a universal is separate from singular things, as the 
aforesaid argument supposed. He describes this problem as "the one with which our analysis 


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is now concerned (235)," i.e., the one which immediately preceded the foregoing argument. 
And he speaks of it in this way: first, that "it is connected with," i.e., is a consequence of, the 
foregoing one, because, as has already been stated, the consideration of the preceding 
question depends on this. For if universals are not separate, they are not principles; but if they 
are separate, they are principles. Second, he speaks of this problem as the most difficult of all 
the problems in this science. This is shown by the fact that the most eminent philosophers 
have held different opinions about it. For the Platonists held that universals are separate, 
whereas the other philosophers held the contrary. Third, he says that this problem is one 
which it is most necessary to consider, because the entire knowledge of substances, both 
sensible and immaterial, depends on it. 

444. For if there is nothing (236). 

Here he advances an argument to show that universals are separate from singular things. For 
singular things are infinite in number, and what is infinite cannot be known. Hence all 
singular things can be known only insofar as they are reduced to some kind of unity which is 
universal. Therefore there is science of singular things only inasmuch as universals are 
known. But science is only about things which are true and which exist. Therefore universals 
are things which exist of themselves apart from singular things. 

445. But if this is (237) 

Then he argues the other side of the question in this way: if it is necessary that universals be 
something apart from singular things, it is necessary that genera exist apart from singular 
things, either the first genera or also the last, which are immediately prior to singular things. 
But this is impossible, as is clear from the preceding discussion. Therefore universals are not 
separate from singular things. 

446. The Philosopher solves this problem in Book VII (659:C 1592) Of this work, where he 
shows in many ways that universals are not substances which subsist of themselves. Nor is it 
necessary, as has often been said, that a thing should have the same mode of being in reality 
that it has when understood by the intellect of a knower. For the intellect knows material 
things immaterially, and in a similar way it knows universally the natures of things which 
exist as singulars in reality, i.e., without considering the principles and accidents of 
individuals. 

447. Further, if there is something (238). 

Here he raises another question, namely, whether anything is separate from things composed 
of matter and form; and in regard to this he does two things. First, he raises the question. 
Second (239:C 448), he proceeds to deal with it ("If, then, there is"). 

In regard to the first it should be observed that he first raises the question whether a universal 
is separate from singular things. Now it happens to be the case that some singular things are 
composed of matter and form. But not all singular things are so composed, either according to 
the real state of affairs, since separate substances are particular because existing and operating 
of themselves, or even according to the opinion of the Platonists, who held that even among 
separate mathematical entities there are particulars inasmuch as they held that there are many 
of them in a single species. And while it is open to dispute whether there is anything separate 
in the case of those things which are not composed of matter and form, as the universal is 
separate from the particular, the problem is chiefly whether there is anything separate in the 


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case of things which are composed of matter and form. Hence he says that the point which 
causes most difficulty is whether there is something "apart from the concrete whole," i.e., 
apart from the thing composed of matter and form. The reason why a composite thing is 
called a concrete whole he explains by adding "when something is predicated of matter." For 
Plato held that sensible matter participates in separate universals, and that for this reason 
universals are predicated of singular things. These participations in universal forms by 
material sensible things constitute a concrete whole inasmuch as a universal form is 
predicated of matter through some kind of participation. Now in regard to these things he 
raises a question which has three parts, namely, whether there is anything that exists apart 
from all things of this kind, or apart from some and not from others, or apart from none. 

448. If, then, there is (239) 

Here he proceeds to deal with this problem; and concerning it he does two things. First, he 
argues against the position that nothing can be held to be separate from things composed of 
matter and form. Second (244:C 454), he argues the other side of the question ("But again if 
anyone holds this"). 

In regard to the first (239) he advances two arguments. First, he argues from the principle that 
those things which are composed of matter and form are sensible things; and therefore he 
proposes that those things which are composed of matter and form are singulars. However, 
singular things are not intelligible but sensible. Therefore, if there is nothing apart from 
singular things which are composed of matter and form, nothing will be intelligible but all 
beings will be sensible. But there is science only of things which are intelligible. Therefore it 
follows that there will be no science of anything, unless one were to say that sensory 
perception and science are the same, as the ancient philosophers of nature held, as is stated in 
Book I of The Soul. But both of these conclusions are untenable, namely, that there is no 
science and that science is sensory perception. Therefore the first position is also untenable, 
namely, that nothing exists except singular things which are composed of matter and form. 

449. Further, neither will anything (240). 

Second, he argues on the grounds that things composed of matter and form are mobile. He 
gives the following argument. All sensible things composed of matter and form perish and are 
subject to motion. Therefore, if there is nothing apart from beings of this kind, it will follow 
that nothing is eternal or immobile. 

450. But if there is (241). 

Here he shows that this conclusion is untenable, namely, that nothing is eternal and immobile. 
He does this, first, with respect to matter; and second (242:C 451), with respect to form 
("Further, since generation"). 

Accordingly, he says first (241) that if nothing is eternal, it is impossible for anything to be 
generated. He proves this as follows. In every process of generation there must be something 
which comes to be and something from which it comes to be. Therefore, if that from which a 
thing comes to be is itself generated, it must be generated from something. Hence there must 
either be an infinite regress in material principles, or the process must stop with some first 
thing which is a first material principle that is ungenerated, unless it might be said, perhaps, 
that it is generated from non-being; but this is impossible. Now if the process were to go on to 
infinity, generation could never be completed, because what is infinite cannot be traversed. 


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Therefore it is necessary to hold either that there is some material principle which is 
ungenerated, or that it is impossible for any generation to take place. 

451. Further, since generation (242). 

Here he proves the same thing with respect to the formal cause; and he gives two arguments, 
the first of which is as follows. Every process of generation and motion must have some 
terminus. He proves this on the grounds that no motion is infinite, but that each motion has 
some terminus. This is clear in the case of other motions which are completed in their termini. 
But it seems that a contrary instance is had in the case of circular motion, which can be 
perpetual and infinite, as is proved in Book VIII of the Physics. And even though motion is 
assumed to be eternal, so that the entire continuity of circular motion is infinite insofar as one 
circular motion follows another, still each circular motion is both complete in its species and 
finite. That one circular motion should follow another is accidental so far as the specific 
nature of circular motion is concerned. 

452. The things which he said about motion in general he proves specially in regard to 
generation; for no process of generation can be infinite, because that thing cannot be 
generated whose process of generation cannot come to an end, since the end of generation is 
to have been made. That its being made is the terminus of generation is clear from the fact 
that what has been generated must exist "as soon as it has come to be," i.e., as soon as its 
generation is first terminated. Therefore, since the form whereby something is, is the terminus 
of generation, it must be impossible to have an infinite regress in the case of forms, and there 
must be some last form of which there is no generation. For the end of every generation is a 
form, as we have said. Thus it seems that just as the matter from which a thing is generated 
must itself be ungenerated because it is impossible to have an infinite regress, in a similar 
way there must be some form which is ungenerated because it is impossible to have an 
infinite regress in the case of forms. 

453. Further, if matter exists (143). 

He gives the second argument, which runs thus. If there is some first matter which is 
ungenerated, it is much more reasonable that there should be some substance, i.e., some form, 
which is ungenerated, since a thing has being through its form, whereas matter is rather the 
subject of generation and transmutation. But if neither of these is ungenerated, then absolutely 
nothing will be ungenerated, since everything which exists has the character of matter or form 
or is composed of both. But it is impossible that nothing should be ungenerated, as has been 
proved (24-2:C 452). Therefore it follows that there must be something else "besides the 
synolon," or concrete whole, i.e., besides the singular thing which is composed of matter and 
form. And by something else I mean the form or specifying principle. For matter in itself 
cannot be separated from singular things, because it has being only by reason of something 
else. But this seems to be true rather of form, by which things have being. 

454. But again if anyone (244). 

Here he argues the other side of the question. For if one holds that there is some form separate 
from singular things which are composed of matter and form, the problem arises in which 
cases this must be admitted and in which not. For obviously this must not be held to be true in 
the case of all things, especially in that of those made by art. For it is impossible that there 
should be a house apart from this sensible house, which is composed of matter and form. 


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455. Now Aristotle solves this problem partly in Book XII (2488) of this work, where he 
shows that there are certain substances separate from sensible things and intelligible in 
themselves; and partly in Book VII (1503), where he shows that the forms or specifying 
principles of sensible things are not separate from matter. However, it does not follow that no 
science of sensible things can be had or that science is sensory perception. For it is not 
necessary that things have in themselves the same mode of being which they have in the 
intellect of one who knows them. For those things which are material in themselves are 
known in an immaterial way by the intellect, as has also been stated above (446). And even 
though a form is not separate from matter, it is not therefore necessary that it should be 
generated; for it is not forms that are generated but composites, as will be shown in Book VII 
(1417) of this work. It is clear, then, in what cases it is necessary to posit separate forms and 
in what not. For the forms of all things which are sensible by nature are not separate from 
matter, whereas the forms of things which are intelligible by nature are separate from matter. 
For the separate substances do not have the nature of sensible things, but are of a higher 
nature and belong to another order of existing things. 


LESSON 10 

Do All Things Have a Single Substance? Do All Things Have the Same or Different 
Principles? 

ARISTOTLE'S TEXT Chapter 4: 999b 20-1000a 

245. Again, there is the problem whether all things, for example, all men, have a single 
substance. 

246. But this is absurd; for not all things whose substance is one are themselves one, but are 
many and different. But this too is untenable. 

247. And at the same time there is the problem how matter becomes each of the many things 
and a concrete whole. 

248. And again one might also raise this problem about principles. For if they are specifically 
one, there will be nothing that is numerically one. Nor again will unity itself and being be 
one. And how will there be science unless there is some unity in all things? 

249. But, on the other hand, if they are numerically one, each of the principles will also be 
one, and not as in the case of sensible things, different for different things; for example, if the 
syllable ba is taken as a species, its principles in every case are specifically the same, for they 
are numerically different. However, if this is not so, but the things which are the principles of 
beings are numerically one, there will be nothing else besides the elements. For it makes no 
difference whether we say "numerically one" or "singular," because it is in this way that we 
say each thing is numerically one. But the universal is what exists in these. For example, if 
the elements of a word were limited in number, there would have to be as many letters as 
there are elements. Indeed, no two of them would be the same, nor would more than two. 

COMMENTARY 


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Q. 11: Are there one or many forms and principles of things? 

456. Having asked what the principles are, and whether some are separate from matter, the 
Philosopher now asks what the principles are like. First (245 :C 456), he asks whether the 
principles are one or many; second (287:C 519), whether they exist potentially or actually 
("And connected with these problems"); and third (290:C 523), whether they are universals or 
singular things ("And there is also the problem"). 

In regard to the first he does two things. First (245:C 456), he inquires how the principles 
stand with respect to unity; and second (266:C 488), what relationship unity has to the notion 
of principle ("But the most difficult"). 

In regard to the first he does three things. First, he inquires specially about the formal 
principle: whether all things that are specifically the same have a single form. Second (248 :C 
46o), he asks the same question of all principles in general ("And again one might"). Third 
(250:C 466), he asks whether corruptible and incorruptible things have the same principles or 
different ones ("Again there is the problem"). 

In regard to the first he does two things. First, he introduces the problem. Second (246:C 
457), he debates it ("But this is absurd"). 

The problem (245), then, is whether all things that belong to the same species, for example, 
all men, have a single substance or form. 

457. But this is absurd (246). 

Then he advances arguments on one side of the question, to show that all things belonging to 
one species do not have a single form. He does this by means of two arguments, the first of 
which runs thus. Things that belong to one species are many and different. Therefore, if all 
things that belong to one species have a single substance, it follows that those which have a 
single substance are many and different. But this is unreasonable. 

458. And at the same time (247) 

Then he gives the second argument , which runs thus. That which is one and undivided in 
itself is not combined with something divided in order to constitute many things. But it is 
evident that matter is divided into different singular things. Hence, if substance in the sense of 
form is one and the same for all things, it will be impossible to explain how each of these 
singular things is a matter having a substance of the kind that is one and undivided, so that as 
a singular thing it is a concrete whole having two parts: a matter and a substantial form which 
is one and undivided. 

459. Now he does not argue the other side of the question, because the very same arguments 
which were advanced above regarding the separateness of universals are applicable in the 
inquiry which follows it against the arguments just given. For if a separate universal exists, it 
must be held that things having the same species have a single substance numerically, 
because a universal is the substance of singular things. Now the truth of this question will be 
established in Book VII (588:C 1356) of this work, where it is shown that the whatness or 
essence of a thing is not other than the thing itself, except in an accidental way, as will be 
explained in that place. 


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460. And again one might (248). 

Here he raises a difficulty concerning the unity of principles in general: whether the principles 
of things are numerically the same, or only specifically the same and numerically distinct. 
And in regard to this he does two things. First, he advances arguments to show that they are 
numerically the same. Second (249:C 464), he argues on the other side of the question ("But, 
on the other hand"). 

In regard to the first (248) he gives three arguments; and he introduces the problem, saying 
that the same question which was raised about substance can be raised about principles in 
general, i.e., whether the principles of things are numerically the same. 

461. He introduces the first argument to show that they are numerically the same. For things 
composed of principles merely contain what they receive from these principles. Therefore, if 
principles are not found to be one numerically but only specifically, the things composed of 
these principles will not be one numerically but only specifically. 

462. The second argument runs thus: unity itself or being itself must be numerically one. And 
by unity itself or being itself he means unity or being in the abstract. Hence, if the principles 
of things are not one numerically but only specifically, it will follow that neither unity itself 
or being itself will subsist of themselves. 

463. The third argument is this: science is had of things because there is found to be a 
one-in-many, as man in common is found in all men; for there is no science of singular things 
but of the unity [i.e., common attribute] found in them. Moreover, all science or cognition of 
things which are composed of principles depends on a knowledge of these principles. If, then, 
principles are not one numerically but only specifically, it will follow that there is no science 
of beings. 

464. But, on the other hand (249). 

Here he argues the opposite side of the question in the following fashion. If principles are 
numerically one so that each of the principles considered in itself is one, it will be impossible 
to say that the principles of beings exist in the same way as the principles of sensible things. 
For we see that the principles of different sensible things are numerically different but 
specifically the same, just as the things of which they are the principles are numerically 
different but specifically the same. We see, for example, that syllables which are numerically 
distinct but agree in species have as their principles letters which are the same specifically 
though not numerically. And if anyone were to say that this is not true of the principles of 
beings, but that the principles of all beings are the same numerically, it would follow that 
nothing exists in the world except the elements, because what is numerically one is a singular 
thing. For what is numerically one we call singular, just as we call universal what is in many. 
But what is singular is incapable of being multiplied, and is encountered only as a singular. 
Therefore, if it is held that numerically the same letters are the principles of all syllables, it 
will fdllow that those letters could never be multiplied so that there could be two of them or 
more than two. Thus a could not be found in these two different syllables ba or da. And the 
argument is the same in the case of other letters. Therefore, by the same reasoning, if the 
principles of all beings are numerically the same, it will follow that there is nothing besides 
these principles. But this seems to be untenable; because when a principle of anything exists it 
will not be a principle unless there is something else besides itself. 


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465. Now this question will be solved in Book XII (2464); for it will be shown there that the 
principles which things have, namely, matter and form or privation, are not numerically the 
same for all things but analogically or proportionally the same. But those principles which are 
separate, i.e., the intellectual substances, of which the highest is God, are each numerically 
one in themselves. Now that which is one in itself and being is God; and from Him is derived 
the numerical unity found in all things. And there is science of these, not because they are 
numerically one in all, but because in our conception there is a one in many. Moreover, the 
argument which is proposed in support of the opposite side of the question is true in the case 
of essential principles but not in that of separate ones, which is the class to which the agent 
and final cause belong. For many things can be produced by one agent or efficient cause, and 
can be directed to one end. 


LESSON 11 

Do Corruptible and Incorruptible Things Have the Same or Different Principles? 
ARISTOTLE'S TEXT Chapter 4: 1000a 5-1001a 3 

250. Again, there is a problem which has been neglected no less by the moderns than by their 
predecessors: whether the principles of corruptible and incorruptible things are the same or 
different. 

25 1 . For if they are the same, how is it that some things are incorruptible and others 
corruptible? And what is the cause? 

252. The followers of Hesiod and all those who were called theologians paid attention only to 
what was plausible to themselves and have neglected us. For,' making the principles of things 
to be gods or generated from the gods, they say that whatever has not tasted nectar and 
ambrosia became mortal. 

253. And it is clear that they are using these terms in a way known to themselves, but what 
they have said about the application of these causes is beyond our understanding. For if it is 
for the sake of pleasure that the gods partake of these things, nectar and ambrosia are not the 
cause of their being. But if they partake of them to preserve their being, how will the gods be 
eternal in requiring food? 

254. But with regard to those who have philosophized by using fables, it is not worth our 
while to pay any serious attention to them. 

255. However, from those who make assertions by means of demonstration it is necessary to 
find out, by questioning them, why some of the things which are derived from the same 
principles are eternal in nature and others are corrupted. But since these philosophers mention 
no cause, and it is unreasonable that things should be as they say, it is clear that the principles 
and causes of these things will not be the same. 

256. For the explanation which one will consider to say something most to the point is that of 
Empedocles, who has been subject to the same error. For he posits a certain principle, hate, 
which is the cause of corruption. 


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257. Yet even hate would seem to generate everything except the one. For all things except 
God are derived from this. Hence he says: "From which have blossomed forth all that was 
and is [and will be]: trees, and men and women, and beasts and flying things, and 
water-nourished fish, and the long-lived gods." And apart from these things it is evident that, 
if hate did not exist in the world, all things would be one, as he says: "For when they have 
come together, then hate will stand last of all." 

258. For this reason too it turns out that God, who is most happy, is less wise than other 
beings. For he does not know all the elements, because hate he does not have, and knowledge 
is of like by like. "For one knows earth by earth, water by water, affection by affection, and 
hate by mournful hate." 

259. But it is also clear (and this is where our discussion began) that hate no more turns out to 
be the cause of corruption than of being. 

260. Nor, similarly, is love the cause of existence; for in blending things together into a unity 
it corrupts other things. 

261. Moreover, he does not speak of the cause of change itself, except to say that it was 
naturally disposed to be so. 

262. [He says]: "But thus mighty hate was nourished among the members and rose to a 
position of honor when the time was fulfilled, which being changeable dissolved the bond." 
Hence change is a necessity, but he gives no reason for its necessity. 

263. Yet he alone speaks expressly to this extent. For he does not make some beings 
corruptible and others incorruptible, but makes all things corruptible ex. cept the elements. 
But the problem that has been stated is why some things are corruptible and others are not, 
supposing that they come from the same principles. To this extent, then, it has been said that 
the principles of things will not be the same. 

264. But if the principles are different, one problem is whether they will be incorruptible or 
corruptible. For supposing that they are corruptible, it is evident that they must also come 
from certain things, because all things that are corrupted are dissolved into those elements 
from which they come. Hence it follows that there are other principles prior to these 
principles. But this is also unreasonable, whether the process stops or goes on to infinity. 
Further, how will corruptible things exist if their principles are destroyed? But if they are 
incorruptible, why will corruptible things come from incorruptible principles, and 
incorruptible things from others? For this is unreasonable, and is either impossible or requires 
a great deal of reasoning. 

265. Further, no one has attempted to say that these things have different principles, but [all 
thinkers] say that all things have the same principles. But they admit the first problem, 
considering it a trifling matter. 

COMMENTARY 

466. Having investigated in a general way whether all principles belonging to one species are 
numerically the same, the Philosopher inquires here whether the principles of corruptible and 
incorruptible things are numerically the same. In regard to this he does three things. First 
(250:C 466), he raises the question. Second (25I:C 467), he introduces an argument to show 


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that the principles of corruptible and those of incorruptible things arc not the same ("For if 
they are the same")- Third (264:C 483), he introduces arguments to show that they are not 
different ("But if the principles"). 

He says first (250), then, that there is a problem which has been neglected no less by the 
modern philosophers, who followed Plato, than by the ancient philosophers of nature, who 
also were puzzled whether the principles of corruptible and incorruptible things are the same 
or different. 

467. For, if they are the same (251). 

Here he advances an argument to show that the principles of corruptible and of incorruptible 
things are not the same. In regard to this he does three things. First (251:C 467), he gives the 
argument. Second (252:C 468), he criticizes the solution of the proposed argument which the 
theological poets gave ("The followers of Hesiod"). Third (255:C 472), he criticizes the 
solution which some philosophers of nature gave ("However, from those who"). 

He says first (251), then, that if the principles of corruptible and of incorruptible things are 
held to be the same, since from the same principles there follow the same effects, it seems 
that either all things are corruptible or all are incorruptible. Therefore the question arises how 
some things are corruptible and others incorruptible, and what the reason is. 

468. The followers of Hesiod (252) 

He criticizes the solution given by the theological poets. First (252:C 468), he gives their 
solution. Second (253 :C 470), he argues against it ("And it is clear that"). Third (254:C 471), 
he gives the reason why he does not criticize this position with more care ("But with regard to 
those"). 

Concerning the first (252) it Must be noted that there were among the Greeks, or philosophers 
of nature, certain students of wisdom, such as Orpheus, Hesiod and certain others, who were 
concerned with the gods and hid the truth about the gods under a cloak of fables, just as Plato 
hid philosophical truth under mathematics, as Simplicius says in his Commentary on the 
Categories.' Therefore he says that the followers of Hesiod, and all those who were called 
theologians, paid attention to what was convincing to themselves and have neglected us, 
because the truth which they understood was treated by them in such a way that it could be 
known only to themselves. For if the truth is obscured by fables, then the truth which 
underlies these fables can be known only to the one who devised them. Therefore the 
followers of Hesiod called the first principles of things gods, and said that those among the 
gods who have not tasted a certain delectable food called nectar or manna became mortal, 
whereas those who had tasted it became immortal. 

469. But some part of the truth could lie hidden under this fable, provided that by nectar or 
manna is understood the supreme goodness itself of the first principle. For all the sweetness 
of love and affection is referred to goodness. But every good is derived from a first good. 
Therefore the meaning of these words could be that some things are incorruptible by reason 
of an intimate participation in the highest good, as those which participate perfectly in the 
divine being. But certain things because of their remoteness from the first principle, which is 
the meaning of not to taste manna and nectar, cannot remain perpetually the same in number 
but only in species, as the Philosopher says in Book II of Generation. But whether they 
intended to treat this obscurely or something else, cannot be perceived any more fully from 


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this statement. 

470. And it is clear (253). 

He argues against the aforesaid position. He says that the meaning which these followers of 
Hesiod wished to convey by the terms nectar or manna was known to them but not to us. 
Therefore their explanation of the way in which these causes are meant to solve this question 
and preserve things from corruption is beyond our understanding. For if these terms are 
understood in their literal sense, they appear to be inadequate, because the gods who tasted 
nectar or manna did so either for the sake of pleasure or because these things were necessary 
for their existence, since these are the reasons why men partake of food. Now if they partook 
of them for the sake of pleasure, nectar and manna could not be the cause of their existence so 
as to make them incorruptible, because pleasure is something that follows on being. But if 
they partook of the aforesaid nourishment because they needed it to exist, they would not be 
eternal, having repeated need of food. Therefore it seems that gods who are first corruptible, 
as it were, standing as they do in need of food, are 'made incorruptible by means of food. This 
also seems to be unreasonable, because food does not nourish a thing according to its species 
unless it is corrupted and passes over into the species of the one nourished. But nothing that is 
corruptible can be responsible for the incorruptibility of something else. 

471. But with regard to those (254). 

Here he gives his reason for not investigating this opinion with more care, He says that it is 
not worth our while to pay any attention to those who have philosophized "by using fables," 
i.e., by hiding philosophical truth under fables. For if anyone argues against their statements 
insofar as they are taken in a literal sense, these statements are ridiculous. But if one wishes to 
inquire into the truth hidden by these fables, it is not evident. Hence it is understood that 
Aristotle, in arguing against Plato and other thinkers of this kind who have treated their own 
doctrines by hiding them under something else, does not argue about the truth which is hidden 
but about those things which are outwardly expressed. 

472. However, from those who make assertions (255). 

Then he argues against the answer given by some of the philosophers of nature; and in regard 
to this he does three things. First (255:C 472), he gives the argument. Second (256:C 473), he 
gives the answer ("For the explanation"). Third (257:C 474), he criticizes it ("Yet even 
hate"). 

Accordingly, he says, first (255), that, having dismissed those who treated the truth by using 
fables, it is necessary to seek information about the aforesaid question from those who have 
treated the truth in a demonstrative way, by asking them why it is that, if all beings are 
derived from the same principles, some beings are eternal by nature and others are corrupted. 
And since these men give no reason why this is so, and since it is unreasonable that things 
should be as they say (that in the case of beings having the same principles some should be 
corruptible and others eternal), it seems clearly to follow that corruptible and eternal things do 
not have the same principles or the same causes. 

473. For the explanation (256). 

Then he gives one solution. He says that the explanation given to the aforesaid question 
which seems to fit it best is the one which Empedocles gave, although he was subject to the 


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same error as the others, because the explanation which he gave is no more adequate than 
theirs, as is about to be shown. For he maintained that corruptible and incorruptible things 
have certain common principles, but that a special principle, hate, causes the corruption of the 
elements in such a way that the coming together of this cause and another principle produces 
corruption in the world. 

474. Yet even hate (257). 

Here he criticizes Empedocles' argument, and he does this in three ways. First (257:C 474), 
he does this by showing that the argument which Empedocles gave is not in keeping with his 
position; second (261 :C 478), by showing that it is not adequate ("Moreover, he does not"); 
third (263 :C 481), by showing that it is not to the point ("Yet he alone speaks"). 

In regard to the first he does three things. First, he shows that Empedocles' argument does not 
agree with his other views about hate; second (258:C 476), that it does not agree with his 
view about God himself ("For this reason"); and third (26o:C 477), that it does not agree with 
his view about love ("Nor, similarly"). 

Accordingly, he says, first (257), that Empedocles' position that hate is the cause of 
corruption is untenable, because according to his position hate also seems to be the cause of 
the generation of all things except one. For he held that everything else is composed 
essentially of hate along with the other principles, with the exception of God alone, whom he 
claimed to be composed of the other principles without hate. Moreover, he called the heavens 
God, as was stated above in Book I (49:C 101), because Xenophanes, after reflecting upon the 
whole heaven, said that the one itself is God. And Empedocles, considering the 
indestructibleness of the heavens, held that the heavens are composed of the four elements 
and love, but not of strife or hatred. But in the case of other things he said that all those which 
are or were or will be, come, from hate, such as sprouting trees, and men and women, and 
beasts (which are terrestial animals), and vultures (which are flying and long-lived animals), 
and fish (which are nourished in the water), and the long-lived gods. And by the gods he 
seems to mean either the stars, which he held are sometimes corrupted, although after a long 
period of time, or the demons, which the Platonists held to be ethereal animals. Or by the 
gods he also means those beings whom the Epicureans held to be of human form, as was 
stated above (210:C 408). Therefore, from the fact that all living things except one are 
generated from hate, it can be said that hate is the cause of generation. 

475. And in addition to this there is another reason [why hate can be said to be the cause of 
generation]; for according to Empedocles' position it is evident that, if hate did not exist in 
the world, all things would be one, since hate is the reason why things are distinct, according 
to Empedocles. Hence he quotes Empedocles' words to the effect that, when all things come 
together into a unity, for example, when chaos comes into being, hate will stand last of all, 
separating and dissolving things. Hence the text of Boethius says: "When it comes together, 
then chaos knows the ultimate discord." Thus it is clear that, since the being of the world 
consists in the distinction of things, hate is the cause of the world's generation. 

476. For this reason (258). 

Here he gives a second argument, which pertains to the deity. He says that, since Empedocles 
would hold that hate is not a constituent of the divine composition, it follows, according to his 
arguments, that God, who is said by all men to be most happy, and consequently most 
knowing, is less prudent than all other beings who have knowledge. For according to 


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Empedodes' position it follows that God does not know the elements because He does not 
contain hate. Hence He does not know himself. And like knows like according to the opinion 
of Empedodes, who said that by earth we know earth, by water water, "and by affection," i.e., 
love or concord, we know affection, or love or concord. And in a similar way we know "hate 
by hate," which is sadness, whether unpleasant or evil, according to the text of Boethius, who 
says that "by evil discord we know discord." It is evident, then, that Aristotle thought this 
untenable and contrary to the position that God is most happy because He himself would not 
know some of the things that we know. And since this argument seemed to be beside the 
point, therefore, returning to his principal theme, he says (259) that, in returning to the point 
from which the first argument began, it is evident, so far as Empedodes is concerned, that 
hate is no more a cause of corruption than of being. 

477. Nor, similarly, is love (260). 

Here he gives the third argument, which pertains to love. He says that in like manner love is 
noe the cause of generation or being, as Empedodes claimed, if another position of his is 
considered. For he said that, when all the elements are combined into a unity, the corruption 
of the world will then take place; and thus love corrupts all things. Therefore, with respect to 
the world in general, love is the cause of corruption, whereas hate is the cause of generation. 
But with respect to singular things, hate is the cause of corruption and love of generation. 

478. Moreover, he does (261). 

Here he shows that Empedodes' argument is not adequate. For Empedodes said that there 
exists in the world a certain alternation of hate and friendship, in such a way that at one time 
love unites all things and afterwards hate separates them. But as to the reason why this 
alternation takes place, so that at one time hate predominates and at another time love, he said 
nothing more than that it was naturally disposed to be so. 

479. And next he gives Empedodes' words, which, because they are written in Greek verse, 
are difficult and differ from the common way of speaking. These words are (262): "But thus 
mighty hate was nourished among the members and rose to a position of honor when the time 
was fulfilled, which being changeable dissolved the bond." But the text of Boethius runs thus: 
"But when mighty discord in the members was promoted to a place of honor, because it 
marched forward in a completed year, which, when these things have been changed, returns 
to a full bond." Now in order to understand this it must be noted that he speaks poetically of 
the whole world as though it were a single living thing in whose members and parts there is 
found at first the greatest harmony, which he calls love or concord, and afterwards there 
begins to exist little by little a certain dissonance, which he calls discord. And, similarly, in 
the parts of the universe at first there was maximum concord, and afterwards hate was 
nourished little by little until it acquired "the place of honor," i.e., it acquired dominion over 
the elements. This comes about when a completed time is reached or a year is completed, as 
Empedodes held, "which" (hate or discord, or the year), being changeable, dissolves "the 
bond," i.e., the former union of the elements; or the year or hate returns to a full bond, 
because by a certain ability and hidden power it returns to predominate over things. 

480. After these words of Empedodes, Aristotle, in giving the meaning of the word 
"changeable" which he used, adds the explanation as though change were necessary; for he 
says that Empedodes made the foregoing statements as though it were necessary that there 
should be an alternation of hate and love, but he gives no reason for this necessity. For in the 
case of this one living thing it is evident that what causes the alternation of hate and love is 


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the motion of the heavens which causes generation and corruption in the world. But no such 
cause can be assigned why the whole should be changed in this way by love and hate. Hence 
it is clear that his argument was inadequate. 

481. Yet he alone (263). 

Here he shows that this argument of Empedocles is not to the point. He says that Empedocles 
seems to say 1 1 expressly," i.e., clearly, only that he does not hold that some of the things 
derived from these principles are corruptible and others incorruptible, but he holds that all 
things are corruptible with the exception of the elements alone. Thus he seems to avoid the 
foregoing problem inasmuch as the question remains why some things are corruptible and 
some not, if they come from the same principles. Hence it is also clear that his argument is 
not to the point, because he neglects the very point that requires explanation. 

482. But it can be asked how he can say here that Empedocles held all things to be corruptible 
except the elements, since Empedocles has said above that the one is God, i.e., what is 
composed of the other principles except hate. It must be noted, however, that Empedocles 
posited two processes of corruption in the world, as is clear from what was said above. He 
posited one with respect to the blending of the whole universe, which was brought about by 
love; and from this process he did not make even God immune, because in God he placed 
love, which caused other things to be mixed with God. And he posited another process of 
corruption for singular things, and the principle of this process is hate. But he excluded this 
kind of corruption from God, seeing that he did not posit hate in God. In summing up, then, 
Aristotle concludes that this much has been said for the purpose of showing that corruptible 
and incorruptible things do not have the same principles. 

483. But if the principles (264) 

Here he argues the other side of the question, with two arguments. The first is this: if the 
principles of corrup41e and incorruptible things are not the same, the question arises whether 
the principles of corruptible things are corruptible or incorruptible. If one says that they are 
corruptible, he proves that this is false by two arguments. The first runs thus: every 
corruptible thing is dissolved into the principles of which it is composed. If, then, the 
principles of corruptible things are corruptible, it will be necessary to hold also that there are 
other principles from which they are derived. But this is untenable, unless an infinite regress 
is posited. Now it was shown in Book II (152:C 299) that it is impossible to have an infinite 
regress in principles in any class of cause. And it would be just as untenable for someone to 
say that this condition applies in the case of corruptible principles, since corruption seems to 
come about as a result of something being dissolved into prior principles. 

484. The second argument runs thus. If the principles of corruptible things are corruptible, 
they must be corrupted, because every corruptible thing will be corrupted. But after they have 
been corrupted they cannot be principles, for what is corrupted or has been corrupted cannot 
cause anything. Therefore, since corruptible things are always caused in succession, the 
principles of corruptible things cannot be said to be corruptible. 

485. Again, if it is said that the principles of corruptible things are incorruptible, evidently the 
principles of incorruptible things are incorruptible. Therefore the question remains why it is 
that from certain incorruptible principles corruptible effects are produced, and from certain 
others incorruptible effects are produced; for this seems to be unreasonable and is either 
impossible or requires considerable explanation. 


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486. Further, no one (265). 

Then relative to his main thesis he gives his second argument, which is drawn from the 
common opinions of all men. For no one has attempted to say that corruptible and 
incorruptible things have different principles, but all say that all things have the, same 
principles. Yet the first argument, given in favor of the first part of the question, all pass over 
lightly, as though it were of little importance; but this is to acknowledge its truth. Hence the 
text of Boethius says: "But they swallow the first argument as though they considered it a 
minor matter." 

Q. 13: Are the principles of corruptible and incorruptible things the same? 

487. Now the solution to this problem is given in Book XII (2553), where the Philosopher 
shows that the first active or motive principles of all things are the same but in a certain 
sequence. For the first principles of things are unqualifiedly incorruptible and immobile, 
whereas the second are incorruptible and mobile, i.e., the celestial bodies, which cause 
generation and corruption in the world as a result of their motion. Now the intrinsic principles 
of corruptible and of incorruptible things are the same, not numerically but analogically. Still 
the intrinsic principles of corruptible things, which are matter and form, are not corruptible in 
themselves but only in reference to something else. For it is in this way that the matter and 
form of corruptible things are corrupted, as is stated in Book I of the Physics. 


LESSON 12 

Are Unity and Being the Substance and Principle of All Things? 
ARISTOTLE'S TEXT Chapter 4: 1001a 4-1001b 25 

266. But the most difficult problem which has to be considered, and the one which is most 
necessary for a knowledge of the truth, is whether unity and being are the substance of 
existing things, and whether each of them is nothing else than unity and being. Or whether it 
is necessary to investigate what being and unity themselves are, as though there were some 
other nature which underlies them. 

267. For some think that reality is of the former sort, and some of the latter. For Plato and the 
Pythagoreans thought that being and unity were nothing else [than themselves] , and that this 
is their nature, their substance being simply unity and being. But among the other 
philosophers [there are different opinions] about the nature of unity. Empedocles, for 
example, as though reducing it to something better known, says that unity is being; for he 
would seem to say that this is love, since this is the cause why unity belongs to all things. 
Others say that this unity and being of which existing things consist and have been made is 
fire, and others say it is air. And those who hold that there are many elements say the same 
thing; for they must also speak of unity and being in as many ways as they say there are 
principles. 

268. But if anyone holds that unity and being are not substances, it will follow that no other 
universals are such; for these are the most universal of all. But if there is no one-in-itself or 
being-in-itself, there will hardly be any other things that exist apart from what are called 


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singular things. Further, if unity is not a substance, evidently number will not exist as another 
reality separate from existing things; for number is units, and a unit is truly something one. 
But if there is a one-in-itself and being-in-itself, the substance of these must be unity itself 
and being itself. For nothing else is predicated universally of all things but these two. 

269. But, on the other hand, if there is to be a one-in-itself and being-in-itself, there is great 
difficulty in seeing how there will be anything else besides these. I mean, how will there be 
more beings than one? For that which differs from being does not exist, Hence according to 
Parmenides' argument it must follow that all beings are one, and that this is being. 

270. But there is a difficulty in either case; for whether unity itself is not a substance, or 
whether there is a unity itself, it is impossible for number to be a substance. Now it has 
already been stated why this follows if unity is not a substance; but if it is, the same difficulty 
will arise with regard to being. For from something outside of being something else will be 
one; for it must be not one. But all beings are either one or many, each of which is a one. 

271. Further, if unity itself is indivisible, according to Zeno's axiom it will be nothing. For 
that which when added does not make a thing greater or when subtracted does not make it 
smaller, this, he says, does not belong to the realm of existing things, as though it were 
evident that whatever has being is a continuous quantity.' And if it is a continuous quantity, it 
is corporeal; for this in every respect is a being. But other quantities, for example, a surface 
and a line, when added in one way will make a thing greater, but in another way they will not; 
and a point and a unit will do so in no way. 

272. But this philosopher speculates clumsily, and it is possible for a thing to be indivisible in 
such a way that some answer may be made against him; for when something of this kind is 
added it will not make a thing greater but more. 

273. Yet how will continuous quantity come from such a unity or from many of them? For 
this would be like saying that a line is made up of points. 

274. But even if someone were to think that the situation is such that number has come, as 
some say, from unity itself and from something else that is not one, none the less it would be 
necessary to inquire why and how the thing which has come to be would sometimes be a 
number and sometimes a continuous quantity, if that not-one were inequality and the same 
nature in either case. For it is not clear how continuous quantities would be produced from 
unity and this principle, or from some number and this principle. 

COMMENTARY 

Q. 14a: Are "one" and "being" substances or principles of things? 

488. Having asked whether the principles of things are the same or different, the Philosopher 
now asks how unity itself could have the nature of a principle; and in regard to this he does 
three things. First, he asks whether unity itself is a principle; second (502), he asks whether 
numbers, which arise or follow from unity, are the principles of things; and third (515), 
whether the Forms, which are certain separate unities, are the principles of things. 

In regard to the first he does three things. First, he raises the question. Second (489), he gives 
the opinions on both sides ("For some think"). Third (490), he advances arguments on both 
sides ("But if anyone"). 


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He says, first (266), that of all the different questions which have been raised, one is more 
difficult to consider because of the weight of the arguments on both sides, and that this 
question is also one about which it is necessary to know the truth, because our decision about 
the substances of things depends on it. Now this question is whether unity and being are the 
substances of things, not so that either of them must be attributed to some other nature which 
would be informed, as it were, by unity and being, but rather so that the unity and being of a 
thing are its substance; or, in an opposite way, whether it is necessary to ask what that thing is 
to which unity and being properly belong, as though there were some other nature which is 
their subject. 

489. For some think (267) 

Here he gives the opinions on each side of the question. He says that some philosophers 
thought that reality was of one kind, and some of another. For Plato and the Pythagoreans did 
not hold that unity and being are the attributes of some nature, but that they constitute the 
nature of things, as though being itself and unity itself were the substance of things. But some 
philosophers, in speaking about the natural world, attributed unity and being to certain other 
natures, as Empedocles reduced the one to something better known, which he- said is unity 
and being; and this seems to be love, which is the cause of unity in the world. But other 
philosophers of nature attributed these to certain elementary causes, whether they posited one 
first principle, as fire or air, or more than one. For since they would hold that the material 
principles of things are the substances of things, it was necessary that each of these should 
constitute the unity and being of things; so that whichever one of these anyone might hold to 
be a principle, he would logically think that through it being and unity would be attributed to 
A things, whether he posited one principle or more than one. 

490. But if anyone (268). 

Here he gives arguments on both sides of the question. First, he gives arguments in support of 
the view of Plato and Pythagoras. Second (269:C 493), he gives arguments on the other side 
of the question, in support of the view of the philosophers of nature ("But, on the other 
hand"). 

In regard to the first (268), he makes use of elimination as follows. It is necessary to hold 
either that unity and being, separate and existing apart, are a substance, or not. Now if it is 
said that unity and being are not a substance, two untenable consequences will follow. The 
first of these is this: unity and being are said to be the most universal of all, and therefore, if 
unity and being are not separate in such a way that unity itself or being itself is a certain 
substance, it will then follow that no universal is separate. Thus it will follow that there is 
nothing in the world except singular things, which seems to be inappropriate, as has been 
stated in earlier questions (C 443). 

491. The other untenable consequence is this. Number is nothing else than units, because 
number is composed of units; for a unit is nothing else than unity itself. Therefore, if unity 
itself is not separate as a substance existing of itself, it will follow that number will not be a 
reality separate from those things which are found in matter. This can be shown to be 
inappropriate in view of what has already been stated above. Hence it cannot be said that 
unity and being are not a substance which exists by itself. 

492. Therefore, if the other part of the division is conceded, that there is something which is 
unity itself and being itself, and that this exists separately, it must be the substance of all those 


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things of which unity and being are predicated. For everything that is separate and is 
predicated of many things is the substance of those things of which it is predicated. But 
nothing else is predicated of all things in as universal a way as unity and being. Therefore 
unity and being will be the substance of all things. 

493. But, on the other hand (269). 

Then he argues the other side of the question; and he gives two arguments. The second 
(271:C 496) of use these begins where he says, "Further, if unity itself." 

In regard to the first he does two things. First, he gives the argument. Second (270:C 494), he 
shows how the question is made difficult as a result of the argument given ("But there is a 
difficulty in either case"). 

The first (269) argument, then, is as follows: if there is something which is itself being and 
unity as something ,existing separately, it will be necessary to say that unity is the very same 
thing as being. But that which differs from being is non-being. Therefore it follows, according 
to the argument of Parmenides, that besides the one there is only non-being. Thus all things 
will have to be one, because it could not be held that that which differs from the one, which is 
essentially separate, is a being. 

494. But there is a difficulty (270). 

Here he shows how this argument creates a difficulty in the case of the position of Plato, who 
held that number is the substance of things. He says that Plato faces a difficulty in either case, 
whether it is said that this separate one is a substance or not. For whichever view is held, it 
seems impossible that number should be the substance of things. For if it is held that unity is 
not a substance, it has already been stated (269:C 493) why number cannot be held to be a 
substance. 

495. But if unity itself is a substance, the same problem will arise with respect to both unity 
and being. For either there is some other unity besides this unity which exists separately of 
itself, or there is not. And if there is no other, a multitude of things will not exist now, as 
Parmenides said. But if there is another unity, then that other unity, since it is not unity itself, 
must have as a material element something that is other than unity itself, and, consequently, 
other than being. And that material element from which this second unity comes to be, will 
have not to be a being. Thus a multitude of beings cannot be constituted from this unity which 
exists apart from unity itself, because all beings are either one or many, each of which is a 
one. But this one has as its material element something that is neither unity nor being. 

496. Further, if unity (271). 

Here he gives the second argument; and in regard to this he does three things. First (271 :C 
496), he gives the argument. Second (272:C 498), he criticizes it ("But this"). Third (273:C 
499), he shows that the difficulty remains ("Yet how will continuous quantity"). 

He says first (271), then, that if this separate unity is indivisible, there follows from this the 
other position, which Zeno assumed, that nothing exists. For Zeno supposed that that which 
when added does not make a thing greater and when taken away does not make it smaller, is 
nothing in the real order. But he makes this assumption on the grounds that continuous 
quantity is the same as being. For it is evident that this is not a continuous quantity — I mean 


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that which when added does not make a thing greater and when subtracted does not make it 
smaller. Therefore, if every being were a continuous quantity, it would follow that that which 
when added does not make a thing greater and when subtracted does not make it smaller, is 
non-being. 

497. And better still, if any particular thing were to bear this out, every being would have to 
be a corporeal continuous quantity. For anything added to or subtracted from a body in any 
one of its dimensions, makes the body greater or less. But other continuous quantities, such as 
lines and surfaces, become greater insofar as one dimension is added, whereas others do not. 
For line added to line in length causes increase in length but not in width; and surface added 
to surface causes increase in width and in length but not in depth. But a point and a unit do 
not become greater or less in any way. Hence according to Zeno's axiom it would follow that 
a point and a unit are non-beings in an absolute sense, whereas a body is a being in every 
respect, and surfaces and lines are beings in one respect and non-beings in another respect. 

498. But this (272). 

Here he criticizes the argument which has been given. He says that Zeno, by proposing such 
an axiom, speculated "clumsily," i.e., in an unskilled and rude manner, so that according to 
him there cannot be anything indivisible. And for this reason some answer must be given to 
the foregoing argument; and if not to the point at issue, at least to the man. Now we say that 
even though a unity when added to something else does not make it larger, it does cause it to 
be more. And it is sufficient for the notion of being that in the case of what is continuous it 
should make a thing larger, and that in the case of what is discrete it should make it more. 

499. Yet how will (273). 

Then he states the difficulty which still faces the Platonists after the above solution. And he 
advances two difficulties. The Ifirst of these is that the Platonists held that the one which is 
indivisible is the cause not only of number, which is a plurality, but also of continuous 
quantity. Therefore, if it is granted that when a one is added it makes a thing more, as would 
seem to suffice for the one which is the cause of number, how will it be possible for 
continuous quantity to come from an indivisible one of this kind, or from many such ones, as 
the Platonists held? For this would seem to be the same thing as to hold that a line is 
composed of points. For unity is indivisible just as a point is. 

500. But even if someone (274) 

Here he gives the second difficulty. He says that if anyone were to think that the situation is 
such that number is the result of the indivisible one and of something else which is not one, 
but participates in the one as a kind of inaterial nature, as some say, the question would still 
remain why and how that which comrs from the one as form and from another material 
nature, which is called the not-one, is sometimes a number and sometimes a continuous 
quantity. The difficulty would be most acute if that material not-one were inequality, as is 
implied in the continuously extended, and were to be the same reality. For it is not clear how 
numbers come from this inequality as matter and from the one as form; nor again is it clear 
how continuous quantities come from some number as form and from this inequality as 
matter. For the Platonists held that number comes from a primary one and a primary two, and 
that from this number and material inequality continuous quantity is produced. 


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501. The solution of this problem is treated by Aristotle in the following books. For the fact 
that there is something separate, which is itself one and being, he will prove below in Book 
XII (2553), when he establishes the oneness of the first principle which is separate in an 
absolute sense, although it is not the substance of all things which are one, as the Platonists 
thought, but is the cause and principle of the unity of all things. And insofar as unity is 
predicated of other things it is used in two ways. In one way it is interchangeable with being, 
and in this way each thing is one by its very essence, as is proved below in Book IV (548); 
and unity in this sense adds nothing to being except merely the notion of undividedness. 
Unity is used in another way insofar as it has the character of a first measure, either in an 
absolute sense or with respect to some genus. And this unity if it is both a minimum in the 
absolute sense and indivisible, is the one which is the principle and measure of number. But if 
it is not both a minimum in an absolute sense and indivisible, it will not be a unit and measure 
in an absolute sense, as a pound in the case of weights and a half-tone in the case of melodies, 
and a foot in the case of lengths. And nothing prevents continuous quantities from being 
composed of this kind of unity. He will establish this in Book X (1940) of this work. But 
because the Platonists thought that the one which is the principle of number and the one 
which is interchangeable with being are the same, they therefore held that the one which is 
the principle of number is the substance of each thing, and consequently that number, 
inasmuch as it is composed of many substantial principles, makes up or comprises the 
substance of composite things. But he will treat this question at greater length in Books XIII 
and XIV of this work. 


LESSON 13 

Are Numbers and Continuous Quantities the Substances and Principles of Sensible Things? 
ARISTOTLE'S TEXT Chapter 5: 1001b 26-1002b 11 

275. And connected with these is the question whether numbers and bodies and surfaces and 
points are substances, or not. 

276. For if they are not, we are in a quandary as to what being is, and what the substances of 
things are. For affections and motions and relations and dispositions and their complex 
conceptions do not seem to signify substance; because all are predicated of some subject, and 
no one of them is a particular thing. And those things which seem to signify substance most 
of all, as fire, water, earth [and air], of which composite bodies are constituted, their heat and 
cold and similar affections, are not substances. And it is only the body which undergoes these 
that remains as a being and is a substance. 

277. Yet a body is a substance to a lesser degree than a surface, and this than a line, and this 
in turn than a unit and a point; for a body is defined by means of these, and these seem to be 
capable of existing without a body, but that a body should exist without these is impossible. 

278. For this reason many of the natural philosophers, including the first, thought that 
substance and being are bodies, and that other things are attributes of this kind of thing; and 
hence too that the principles of bodies are the principles of beings. But the later philosophers, 
who were wiser than these, thought that the principles-of things are numbers. Therefore, as 
we have said, if these are not substance, there is no substance or being at all; for the accidents 


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of these things are not worthy to be called beings. 

279. But if it is admitted that lengths and points are substances to a greater degree than 
bodies, and we do not see to what sort of bodies these belong (because it is impossible for 
them to exist in sensible bodies), there will then be no substance at all. 

280. Further, all of these seem to be dimensions of bodies, one according to width, another 
according to depth, and another according to length. 

281. And, similarly, any figure whatever already exists in a solid. Hence if neither Mercury is 
in the stone, nor one half of a cube in a cube as something segregated, neither will surface 
exist in a solid; for if this were true of anything whatever, it would also be true of that which 
divides a thing in half. And the same argument would apply in the case of a line, a point and a 
unit. If, then, a body is substance in the highest degree, and these things are such to a greater 
degree than it is, and these do not exist and are not substances, it escapes our understanding as 
to what being itself is and what the substance of beings is. 

282. For along with what has been said there happen to be certain unreasonable views about 
generation and corruption. For if substance, not existing before, exists now, or existing 
before, does not exist afterwards, it seems to suffer these changes through generation and 
corruption. But it is impossible for points and lines and surfaces either to come to be or to be 
destroyed, even though they sometimes exist and sometimes do not. For when bodies are 
joined or divided, at one time, when they are joined, they [i.e., the two surfaces] 
simultaneously become one, and at another time, when they are divided, two surfaces are 
produced; because it [i.e., one of the two surfaces in question] is not in the bodies which have 
been joined but has perished. And when bodies are divided surfaces exist which did not exist 
before. For the indivisible point is not divided into two, and if things are generated and 
corrupted, they are generated from something. 

283. And it is similar with regard to the now in time, for this cannot be generated and 
corrupted. Yet it seems always to exist, although it is not a substance. It is also clear that this 
is true of points, lines and surfaces, because the argument is the same; for they are all 
similarly either limits or divisions. 

COMMENTARY 

Q 14b: Are numbers and continuous quantities the substances or principles of sensible 
things? 

502. Having inquired whether unity and being are the substances of sensible things, the 
Philosopher now asks whether numbers and continuous quantities are the substances of 
sensible things; and in regard to this he does three things. First (502), he presents the 
question. Second (503), he argues in support of one side of the question ("For if they are 
not"). Third (507), he argues on the other side ("But if it is admitted"). 

Accordingly he says, first, that "connected with these," i.e., following from the foregoing 
problem, there is the question whether numbers and continuous quantities, i.e., bodies, 
surfaces, and their extremities, such as points, are either substances that are separate from 
sensible things, or are the substances of sensible things themselves, or not. He says that this 
problem is a result of the foregoing one, because in the foregoing problem it was asked 
whether unity is the substance of things. Now unity is the principle of number. But number 


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seems to be the substance of continuous quantity inasmuch as a point, which is a principle of 
continuous quantity, seems to be merely the number one having position, and a line to be the 
number two having position, and the primary kind of surface to be the number three having 
position, and a body the number four having position. 

503. For if they are not (276). 

Then he advances an argument to show that these are the substances of sensible things; and in 
regard to this he does two things. First (276:C 503), he introduces an argument to show that 
these are the substances of sensible things. Second (278 :C 506), he shows how the early 
philosophers followed out the first arguments ("For this reason"). 

In regard to the first he does two things. For, first, he advances an argument to show that body 
is the substance of things; and second (277:C 504), to show that many other things are 
substances to an even greater degree ("Yet a body"). 

He says, first (276), that if these things are not substances, we are in a quandary as to what 
being is essentially, and what the substances of beings are. For it is evident that affections and 
motions and relations and dispositions or arrangements, and their complex conceptions ' 
according as they are put into words, do not seem to signify the substance of anything; 
because all things of this kind seem to be predicated of a subject as something belonging to 
the genus of quantity, and no one of them seems to signify "this particular thing," i.e., 
something that is complete and subsists of itself. This is especially evident in regard to the 
foregoing things, which are not said to be complete things but things whose nature consists in 
a kind of relation. But of all things those which especially seem to signify substance are fire, 
earth, and water, of which many bodies are composed. But he omits air, because it is less 
perceptible; and this is the reason why some thought air to be nothing. But in these bodies 
there are found certain dispositions, namely, hot and cold and other affections and passible 
qualities of this kind, which are not substances according to what has been said. It follows, 
then, that body alone is substance. 

504. Yet a body (277) 

Here he proceeds to examine those things which appear to be substance to an even greater 
degree than a body. He says that a body seems to be a substance to a lesser degree than a 
surface, and a surface than a line, and a line than a point or a unit. He proves this in two ways, 
of which the first is as follows. That by which a thing is defined seems to be its substance, for 
a definition signifies substance. But a body is defined by a surface, a surface by a line, a line 
by a point, and a point by a unit, because they say that a point is a unit having position. 
Therefore surface is the substance of body, and so on for the others. 

505. The second argument runs as follows. Since substance is the primary kind of being, 
whatever is prior seems to be substance to a greater degree. But a surface is naturally prior to 
a body, because a surface can exist without a body but not a body without a surface. 
Therefore a surface is substance to a greater degree than a body. The same reasoning can be 
applied to all the others in turn. 

506. For this reason (278). 

Then he shows how the earlier philosophers followed out the foregoing arguments. He says 
that it was because of the foregoing arguments that many of the ancient philosophers, 


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especially the first, thought that body alone was being and substance, and that all other things 
were accidents of bodies. Hence when they wanted to study the principles of beings, they 
studied the principles of bodies, as was stated above in Book I (36:C 74) with regard to the 
positions of the ancient natural philosophers. But the other philosophers who came later, and 
were reputed to be wiser than the aforesaid philosophers inasmuch as they dealt more 
profoundly with the principles of things, i.e., the Pythagoreans and Platonists, were of the 
opinion that numbers are the substances of sensible things inasmuch as numbers are 
composed of units. And the unit seems to be one substance of things. Hence, according to the 
foregoing arguments and opinions of the philosophers, it seems that if these things — numbers, 
lines, surfaces, and bodies — are not the substances of things, there will be no being at all. For 
if these are not beings, it is unfitting that their accidents should be called beings. 

507. But if it is (279). 

Then he argues in support of the other side of the question; and he gives four arguments, the 
first of which is as follows. If anyone were to admit that lengths and points are substances to a 
greater degree than bodies, then supposing that things of this sort are not substances, it also 
follows that bodies are not substances. Consequently, no substance will exist, because the 
accidents of bodies are not substances, as has been stated above (C 503). But points, 'lines and 
surfaces are not substances. For these must be the limits of some bodies, because a point is 
the limit of a line, a line the limit of a surface, and a surface the limit of a body. But it is not 
evident to what sort of bodies these surfaces, lines and points, which are substances, belong. 
For it is evident that the lines and surfaces of sensible bodies are not substances, because they 
are altered in the same way as the other accidents in reference to the same subject. Therefore 
it follows that there will be no substance whatever. 

508. Further, all of these (280). 

Here he gives the second argument, which is as follows. All of the abovementioned things 
seem to be certain dimensions of bodies, either according to width, as a surface, or according 
to depth, as a solid, or according to length, as a line. But the dimensions of a body are not 
substances. Therefore things of this kind are not substances. 

509. And, similarly (281). 

Here he gives a third argument, which is as follows. Any figure which can be educed from a 
solid body according to some dimension is present in that body in the same way, i.e., 
potentially. But in the case of a large piece of stone which has not yet been cut, it is evident 
that "Mercury," i.e., the figure of Mercury, is not present in it actually but only potentially. 
Therefore, in like manner, "in a cube," i.e., in a body having six square surfaces, one half of 
the cube, which is another figure, is not present actually; but it becomes actual in this way 
when a cube has already been divided into two halves. And since every eduction of a new 
figure in a solid which has been cut is made according to some surface which limits a figure, 
it is also evident that such a surface will not be present in a body actually but only potentially. 
For if each surface besides the external one were actually present in a solid body, then for the 
same reason the surface which limits one half of the figure would also be actually present in 
it. But what has been said of a surface must also be understood of a line, a point, and a unit; 
for these are actually present in the continuum only insofar as they limit the continuum, and it 
is evident that these are not the substance of a body. But the other surfaces and lines cannot 
be the substance of a body, because they are not actually present in it; for a substance is 
actually present in the thing whose substance it is. Hence he concludes that of all of these 


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body especially seems to be substance, and that surfaces and lines seem to be substance to a 
great degree than bodies. Now if these are not actual beings or substances, it seems to escape 
our comprehension as to what being is and what the substances of things are. 

510. For along with (282). 

Here he gives the fourth argument. First, he states it, and second (283 :C 513), he clarifies it 
by using a similar case ("And it is similar"). 

Accordingly, he says, first (282), that along with the other untenable consequences mentioned 
there also happen to be certain unreasonable views about generation and corruption on the 
part of those who hold that lines and surfaces are the substances of sensible things. For every 
substance which at first did not exist and later does exist, or which first was and afterwards is 
not, seems to suffer this change by way of generation and corruption. This is most evident in 
the case of all those things which are caused by way of motion. But points and lines and 
surfaces sometimes are and sometimes are not. Yet they are not generated or corrupted. 
Neither, then, are they substances. 

511. He then proves each assumption. The first of these, is that they sometimes are and 
sometimes are not. For it happens that bodies which were at first distinct are afterwards 
united, and that those which were at first united are afterwards divided. For when bodies 
which were initially separated are united, one surface is produced for the two of them, 
because the parts of a continuous body are united in having one common boundary, which is 
one surface. But when one body is divided into two, two surfaces are produced, because it 
cannot be said that when two bodies are brought together their surfaces remain intact, but that 
both "perish," i.e., cease to be. In like manner, when bodies are divided there begin to exist 
for the first time two surfaces which previously did not exist. For it cannot be said that a 
surface, which is indivisible according to depth, is divided into two surfaces according to 
depth; or that a line, which is indivisible according to width, is divided according to width; or 
that a point, which is indivisible in every respect, is divided in any respect whatsoever. Thus 
it is clear that two things cannot be produced from one thing by way of division, and that one 
thing cannot be produced from two of these things by way of combination. Hence it follows 
that points, lines and surfaces sometimes begin to be and sometimes cease to be. 

512. After having proved this, he proves the second assumption, namely, that these things are 
neither generated nor corrupted. For everything that is generated is generated from something, 
and everything that is corrupted is dissolved into something as its matter. But it is impossible 
to assign any matter whatever from which these things are generated and into which they are 
dissolved, because they are simple. Therefore they are neither generated nor corrupted. 

513. And it is similar (283). 

Then he makes the foregoing argument clear by using a similar case. For the now in time 
stands to time as a point to a line. But the now in time does not seem to be generated and 
corrupted, because if it were its generation and corruption would have to be measured by 
some particular time or instant. Thus the measure of this now either would be another now 
and so on to infinity, or would be time itself. But this is impossible. And even though the now 
is not generated or corrupted, still each now always seems to differ, not substantially but 
existentially, because the substance of the now corresponds to the mobile subject. But the 
difference of the now in terms of existence corresponds to the variation in motion, as is 
shown in Book IV of the Physics. Therefore the same thing seems to be true of a point in 


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relation to a line, and of a line in relation to a surface, and of a surface in relation to a body, 
namely, that they are neither corrupted nor generated, although some variation is observable 
in things of this kind. For the same holds true of all of these, because all things of this kind 
are, in like manner, limits if regarded as at the extremities, or divisions if they are found in 
between. Hence, just as the now varies existentially as motion flows by, although it remains 
substantially the same because the mobile subject remains the same, so also does the point 
vary. And it does not become different because of the division of a line, even though it is not 
corrupted or generated in an absolute sense. The same holds true of the others. 

514. But the Philosopher will treat this question in Books XIII and XIV. And the truth of the 
matter is that mathematical entities of this kind are not the substances of things, but are 
accidents which accrue to substances. But this mistake about continuous quantities is due to 
the fact that no distinction is made between the sort of body which/belongs to the genus of 
substance and the sort which belongs to the genus of quantity. For body belongs to the genus 
of substance according as it is composed of matter and form; and dimensions are a natural 
consequence of these in corporeal matter. But dimensions themselves belong to the genus of 
quantity, and are not substances but accidents whose subject is a body composed of matter 
and form. The same thing too was said above (500) about those who held that numbers are the 
substances of things; for their mistake came from not distinguishing between the one which is 
the principle of number and that which is interchangeable with being. 


LESSON 14 

Are There Separate Forms in Addition to the Objects of Mathematics and Sensible Things? 
ARISTOTLE'S TEXT Chapter 6: 1002b 12-1002b 32 

284. But in general one will wonder why, in addition to sensible things and those which are 
intermediate, it is necessary to look for certain other things which we posit as the specific 
essences (or Forms) of sensible things. 

285. For if it is because the objects of mathematics differ in one respect from the things which 
are at hand, they do not differ in being many things that are specifically the same. Hence the 
principles of sensible things will not be limited in number but only in species; unless one 
were to consider the principles of this particular syllable or word, for these are limited in 
number. And this is likewise true of the intermediate entities; for in their case too there are an 
infinite number of things that are specifically the same. Hence, if in addition to sensible 
substances and the objects of mathematics there are not certain other things, such as some call 
the Forms, there will be no substance which is one both numerically and specifically. Nor will 
the principles of beings be limited in number, but only in species. Therefore, if this is 
necessary, it will also be necessary on this account that there should be Forms. And even if 
those who speak of the Forms do not express themselves clearly, although this is what they 
wanted to say, they must affirm that each of the Forms is a substance, and that nothing 
accidental pertains to them. 

286. But if we hold that the Forms exist, and that principles are one numerically but not 
specifically, we have stated the untenable conclusions that follow from this view. 


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COMMENTARY 

Q14c: Are forms substances or principles of things? 

515. Having inquired whether the objects of mathematics are the principles of sensible 
substances, the Philosopher now inquires whether in addition to the objects of mathematics 
there are certain other principles, such as those which we call Forms, which are the 
substances and principles of sensible things. In regard to this he does three things. First, he 
presents the question. Second (516), he argues one side of the question ("For if it is 
because"). Third (518), he argues the other side ("But if we hold"). 

Accordingly, he says, first, that if one assumes that the objects of mathematics are not the 
principles of sensible things and their substances, one will next have the problem why, in 
addition to both sensible things and the objects of mathematics (which are an intermediate 
class between sensible things and the Forms), it is necessary to posit a third class of entities, 
namely, the specific essences, i.e., the Ideas or separate Forms. 

516. For if it is because (285) 

Here he argues one side of the question. The reason why it is necessary to posit separate 
Forms over and above sensible substances and the objects of mathematics seems to be that the 
objects of mathematics differ in one respect "from the things at hand," i.e., from sensible 
things, which exist in the universe; for the objects of mathematics abstract from sensible 
matter. Yet they do not differ but rather agree in another respect. For just as we find many 
sensible things which are specifically the same but numerically different, as many men or 
many horses, in a similar way we find many objects of mathematics which are specifically the 
same but numerically different, such as many equilateral triangles and many equal lines. And 
if this is true, it follows that, just as the principles of sensible things are not limited in number 
but in species, the same thing is true "of the intermediate entities" — the objects of 
mathematics. For since in the case of sensible things there are many individuals of one 
sensible, species, it is evident that the principles of sensible things are not limited in number 
but in species, unless of course we can consider the proper principles of a particular 
individual thing, which are also limited in number and are individual. He gives as an example 
words; for in the case of a word expressed in letters it is clear that the letters are its principles, 
yet there are not a limited number of individual letters taken numerically, but only a limited 
number taken specifically, some of which are vowels and some consonants. But this 
limitation is according to species and not according to number. For a is not only one but 
many, and the same applies to other letters. But if we take those letters which are the 
principles of a particular syllable, whether written or spoken, then they are limited in number. 
And for the same reason, since there are many objects of mathematics which are numerically 
different in one species, the mathematical principles of mathematical science could not be 
limited in number but only in species. We might say, for example, that the principles of 
triangles are three sides and three angles; but this limitation is according to species, for any of 
them can be multiplied to infinity. Therefore, if there were nothing besides sensible things 
and the objects of mathematics, it would follow that the substance of a Form would be 
numerically one, and that the principles of beings would not be limited in number but only in 
species. Therefore, if it is necessary that they be limited in number (otherwise it would 
happen that the principles of things are infinite in number), it follows that there must be 
Forms in addition to the objects of mathematics and sensible things. 


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517. This is what the Platonists wanted to say, because it necessarily follows from the things 
which they held that in the case of the substance of sensible things there is a single Form to 
which nothing accidental belongs. For something accidental, such as whiteness or blackness, 
pertains to an individual man, but to this separate man, who is a Form, according to the 
Platonists, there pertains nothing accidental but only what belongs to the definition of the 
species. And although they wanted to say this, they did not "express themselves" clearly; i.e., 
they did not clearly distinguish things. 

518. But if wehold that (286). 

Then he counters with an argument for the other side of the question. He says that, if we hold 
that there are separate Forms and that the principles of things are limited not only in species 
but also in number, certain impossible consequences will follow, which are touched on above 
in one of the questions (464). 

But the Philosopher will deal with this problem in Book XII (2450) and Book XIV of this 
work. And the truth of the matter is that, just as the objects of mathematics do not exist apart 
from sensible things, neither do Forms exist apart from the objects of mathematics and from 
sensible substances. And while the efficient and moving principles of things are limited in 
number, the formal principles of things, of which there are many individuals in one species, 
are not limited in number but only in species. 


LESSON 15 

Do First Principles Exist Actually or Potentially, and Are They Universal or Singular? 
ARISTOTLE'S TEXT Chapter 6: 1002b 32-1003b 17 

287. And connected with these problems there is the question whether the elements of things 
exist potentially or in some other way. 

288. If they exist in some other way, then there will be something else prior to [first] 
principles. For potentiality is prior to that cause, but the potential need not exist in that way. 

289. But if the elements exist potentially, it is possible for nothing to exist; for even that 
which does not yet exist is capable of existing, because that which does not exist may come to 
be. But nothing that is incapable of existing may come to be. It is necessary, then, to 
investigate these problems. 

290. And there is also the problem whether [first] principles are universals or singular things, 
as we maintain. 

291. For if they are universals, they will not be substances, because a common term signifies 
not a particular thing but what sort of thing; and a substance is a particular thing. 

292. But if it is a particular thing, and is held to be the common whatness which is predicated 
of things, Socrates himself will be many animals: [himself] and man and animal; i.e., if each 
of these signifies a particular thing and a one. If, then, the first principles of things are 


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universals, these consequences will follow. 

293. However, if they are not universals but have the nature of singular things, they will not 
be knowable; for all scientific knowledge is universal. Hence, if there is to be any scientific 
knowledge of [first] principles, there will have to be different principles which are predicated 
universally and are prior to [first] principles. 

COMMENTARY 

Q 14d: Are principles of substances actual or potential? 

519. Having inquired what the principles are, the Philosopher now asks how they exist. First, 
he asks whether they exist potentially or actually; and second (523), whether they are 
universals or singulars ("And there is also the problem"). In regard to the first he does three 
things. First, he raises the question. Second (520), he argues one side ("If they exist"). Third 
(501), he argues the opposite side ("But if the elements"). 

His first question (287), then, is whether first principles exist potentially or "in some other 
way," i.e., actually. This problem is introduced because of the ancient philosophers of nature, 
who held that there are only material principles, which are in potency. But the Platonists, who 
posited separate Forms as formal principles, claimed that they exist actually. 

520. If they exist (288). 

He proves that principles exist potentially. For if they were to exist "in some other way," i.e., 
actually, it would follow that there would be something prior to principles; for potentiality is 
prior to actuality. This is clear from the fact that one thing is prior to another when the 
sequence of their being cannot be reversed; for if a thing exists, it follows that it can be, but it 
does not necessarily follow that, if a thing is possible, it will exist actually. But it is 
impossible for anything to be prior to a first principle. Therefore it is impossible for a first 
principle to exist in any other way than potentially. 

521. But if the elements (289). 

Here he argues the other side of the question. If the principles of things exist potentially, it 
follows that no beings exist actually; for that which exists potentially does not yet exist 
actually. He proves this on the grounds that that which is coming to be is not a being. For that 
which exists is not coming to be; but only that comes to be which exists potentially. Therefore 
everything that exists potentially is nonbeing. Hence if principles exist only potentially, 
beings will not exist. But if principles do not exist, neither will their effects. It follows, then, 
that it is possible for nothing to exist in the order of being. And in summing this tip he 
concludes that according to what has been said it is necessary to inquire about the principles 
of things for the reasons given. 

522. This question will be answered in Book IX (1844) of this work, where it is shown that 
actuality is prior to potentiality in an unqualified sense, but that in anything moved from 
potentiality to actuality, potentiality is prior to actuality in time. Hence it is necessary that the 
first principle exist actually and not potentially, as is shown in Book XII (2500) of this work. 

Q 14e: Are principles of substances universal or singular? 


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523. And here is also the problem (290). 

Here he asks whether the principles of things exist as universals or as singular things; and in 
regard to this he does three things. First, he presents the question. Second (524), he argues 
one side ("For if they are universals"). Third (527), he argues the other side ("However, if 
they are not universals"). The problem (290), then, is whether principles are universals or 
exist in the manner of singular things. 

524. For if they are (291). 

Then he proves that principles are not universals, by the following argument. No predicate 
common to many things signifies a particular thing, but signifies such and such a thing or of 
what sort a thing is; and it does this not according to accidental quality but according to 
substantial quality, as is stated below in Book V (487:C 987) of this work. The reason for this 
is that a particular thing is said to be such insofar as it subsists of itself. But that which 
subsists of itself cannot be something that exists in many, as belongs to the notion of 
common. For that which exists in many will not subsist of itself unless it is itself many. But 
this is contrary to the notion of common, because what is common is what is onein-many. 
Hence it is clear that a particular thing does not signify anything common, but signifies a 
form existing in many things. 

525. Further, he adds the minor premise, namely, that substance signifies a particular thing. 
And this is true of first substances, which are said to be substances in the full and proper 
sense, as is stated in the Categories; " for substances of this kind are things which subsist of 
themselves. Thus it follows that, if principles are universals, they are not substances. Hence 
either there will be no principles of substances, or it will be necessary to say that the 
principles of substances are not substances. 

526. But since it is possible for someone to affirm that some common predicate might signify 
this particular thing, he therefore criticizes this when he says "But if it is (292)." 

He explains the untenable consequence resulting from this. For if a common predicate were a 
particular thing, it would follow that everything to which that common predicate is applied 
would be this particular thing which is common. But it is clear that both animal and man are 
predicated of Socrates, and that each of these — animal and man — is a common predicate. 
Hence, if every common predicate were a particular thing, it would follow that Socrates 
would be three particular things; for Socrates is Socrates, which is a particular thing; and he is 
also a man, which is a particular thing according to the above; and he is also an animal, which 
is similarly a particular thing. Hence he would be three particular things. Further, it would 
follow that there would be three animals; for animal is predicated of itself, of man, and of 
Socrates. Therefore, since this is impossible, it is also impossible for a common predicate to 
be a particular thing. These, then, will be the impossible consequences which follow if 
principles are universals. 

527. However, if they are not (293). 

He argues the other side of the question. Since all sciences are universal, they are not 
concerned with singulars but with universals. Therefore, if some principles were not 
universals but were singular things, they would not be knowable in themselves. Hence, if any 
science were to be had of them, there would have to be certain prior principles, which would 
be universals. It is necessary, then, that first principles be universals in order that science may 


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be had of things; because if principles remain unknown, other things must remain unknown. 

528. This question will be answered in Book VII (1584) of this work, where it is shown that 
universals are neither substances nor the principles of things. However, it does not follow for 
this reason that, if the principles and substances of things were singulars, there could be no 
science of them, both because immaterial things, even though they subsist as singulars, are 
nevertheless also intelligible, and also because there is science of singulars according to their 
universal concepts which are apprehended by the intellect. 


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METAPHYSICS 
BOOK IV 

THE SUBJECT OF METAPHYSICS, 
DEMONSTRATIVELY 


CONTENTS 

The Proper Subject Matter of This Science: Being as Being, and Substance 
and Accidents 

This Science Considers Being and Unity. The Parts of Philosophy Based on 
the Divisions of Being and Unity 

The Same Science Considers Unity and Plurality and All Opposites. The 
Method of Treating These 

First Philosophy Considers All Contraries. Its Distinction from Logic 

Answers to Questions Raised in Book III about Principles of Demonstration 

First Philosophy Must Examine the First Principle of Demonstration. The 
Nature of This Principle. The Errors about It 

Contradictories Cannot Be True at the Same Time 

Other Arguments Against the Foregoing Position 

Three Further Arguments Against Those Who Deny the First Principle 

The Procedure Against Those Who Say that Contradictories Are True at the 
Same Time 

The Reason Why Some Considered Appearances to Be True 

Two Reasons Why Some Identify Truth with Appearances 

Change in Sensible Things Not Opposed to Their Truth 

Seven Arguments against the View that Truth Consists in Appearances 

Refutation of the View that Contradictories Can Be Shown to Be True at the 
Same Time. Contraries Cannot Belong to the Same Subject at the Same 
Time 

No Intermediate between Contradictories. How Heraclitus and Anaxagoras 
Influenced This Position 

Rejection of the opinions that Everything Is True and False, and that 
Everything Is at Rest and in Motion 


LESSON 1 

The Proper Subject Matter of This Science: Being as Being, and Substance and Accidents 
ARISTOTLE'S TEXT Chapters 1 & 2: 1003a-1003b 22 

294. There is a certain science which studies being as being and the attributes which 
necessarily belong to being. 

METAPHYSICSBOOK IV 


LESSON 1: 
LESSON 2 

LESSON 3 

LESSON 4 
LESSON 5 

LESSON 6 

LESSON 7 
LESSON 8 
LESSON 9 

LESSON 10 

LESSON 11 
LESSON 12 
LESSON 13 
LESSON 14 

LESSON 15 

LESSON 16 
LESSON 17 


Thomas Aquinas: Commentary on Aristotle's Metaphysics: English 

295. This science is not the same as any of the so-called particular sciences; for none of the 
other sciences attempt to study being as being in general, but cutting off some part of it they 
study the accidents of this part. This, for example, is what the mathematical sciences do. 

296. Now since we are seeking the principles and ultimate causes of things, it is evident that 
these must be of themselves the causes of some nature. Hence, if those who sought the 
elements of beings sought these principles, they must be the elements of beings not in any 
accidental way but inasmuch as they are beings. Therefore the first causes of being as being 
must also be understood by us. 

Chapter 2 

297. The term being is used in many senses, but with reference to one thing and to some one 
nature and not equivocally. Thus everything healthy is related to health, one thing because it 
preserves health, another because it causes it, another because it is a sign of it (as urine) and 
still another because it is receptive of it. The term medical is related in a similar way to the art 
of medicine; for one thing is called medical because it possesses the art of medicine, another 
because it is receptive of it, and still another because it is the act of those who have the art of 
medicine. We can take other words which are used in a way similar to these. And similarly 
there are many senses in which the term being is used, but each is referred to a first principle. 
For some things are called beings because they are substances; others because they are 
affections of substances; others because they are a process toward substance, or corruptions or 
privations or qualities of substance, or because they are productive or generative principles of 
substance, or of things which are related to substance, or the negation of some of these or of 
substance. For this reason too we say that non-being is non-being. 

298. Therefore, just as there is one science of all healthy things, so too the same thing is true 
in other cases. For it is the office of one and the same science to study not only those things 
which are referred to one thing but also those which are referred to one nature. For those too 
in a sense are referred to one thing. 

299. It is evident, then, that it is the function of one science to study beings as beings. 

299a. But in every respect a science is concerned with what is primary, and that on which 
other things depend, and form which they derive their name. Hence, if this is substance, it 
must be of substances that the philosopher possesses the principles and causes. 

300. Now of every single class of things there is one sense and one science; for example, 
grammar, which is one science, studies all words. And for this reason too it belongs to a 
general science to study all species of being as being and the species of these species. 

COMMENTARY 

It is being and its properties 

529. In the preceding book the Philosopher proceeded to treat dialectically the things which 
ought to be considered in this science. Here he begins to proceed demonstratively by 
establishing the true answer to those questions which have been raised and argued 
dialectically. 


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In the preceding book he treated dialectically both the things which pertain to the method of 
this science, namely, those to which the consideration of this science extends, as well as those 
which fall under the consideration of this science. And because it is first necessary to know 
the method of a science before proceeding to consider the things with which it deals, as was 
explained in Book II (335), this, part is therefore divided into two members. First, he speaks 
of the things which this science considers; and second (749), of those which fall under its 
consideration. He does this in Book V ("In one sense the term principle"). 

The first part is divided into two members. First, he establishes what the subject matter of this 
science is. Second (534), he proceeds to answer the questions raised in the preceding book 
about the things which this science considers ("The term being"). 

In regard to the first he does three things. First, he submits that there is a science whose 
subject is being. Second (532), he shows that it is not one of the particular sciences ("But this 
science"); and third (533), he shows that it is the science with which we are now dealing 
("Now since"). 

Now because a science should investigate not only its subject but also the proper accidents of 
its subject, he therefore says, first, that there is a science which studies being as being, as its 
subject, and studies also "the attributes which necessarily belong to being," i.e., its proper 
accidents. 

530. He says "as being" because the other sciences, which deal with particular beings, do 
indeed consider being (for all the subjects of the sciences are beings), yet they do not consider 
being as being, but as some particular kind of being, for example, number or line or fire or the 
like. 

531. He also says "and the attributes which necessarily belong to being," and not just those 
which belong to being, in order to show that it is not the business of this science to consider 
those attributes which belong accidentally to its subject, but only those which belong 
necessarily to it. For geometry does not consider whether a triangle is of bronze or of wood, 
but only considers it in an absolute sense according as it has three angles equal to two right 
angles. Hence a science of this kind, whose subject is being, must not consider all the 
attributes which belong accidentally to being, because then it would consider the accidents 
investigated by all sciences; for all accidents belong to some being, but not inasmuch as it is 
being. For those accidents which are the proper accidents of an inferior thing are related in an 
accidental way to a superior thing; for example, the proper accidents of man are not the 
proper accidents of animal. 

Now the necessity of this science, which considers being and its proper accidents, is evident 
from this, that such things should not remain unknown since the knowledge of other things 
depends on them, just as the knowledge of proper objects depends on that of common objects. 

532. This science (295). 

Then he shows that this science is not one of the particular sciences, and he uses the following 
argument. No particular science considers universal being as such, but only some part of it 
separated, from the others; and about this part it studies the proper accidents. For example, the 
mathematical sciences study one kind of being, quantitative being. But the common science 
considers universal being as being, and therefore it is not the same as any of the particular 
sciences. 


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533. Now since (296). 

Here he shows that the science with which we are dealing has being as its subject, and he uses 
the following argument. Every principle is of itself the principle and cause of some nature. 
But we are seeking the first principles and utlimate causes of things, as was explained in 
Book I (57), and therefore these are of themselves the causes of some nature. But this nature 
can only be the nature of being. This is clear from the fact that all philosophers, in seeking the 
elements of things inasmuch as they are beings, sought principles of this kind, namely, the 
first and ultimate ones. Therefore in this science we are seeking the principles of being as 
being. Hence being is the subject of this science, for any science seeks the proper causes of its 
subject. 

It applies analogically to the different categories. 

534. The term "being" (297). 

Then he proceeds to answer the questions raised in the preceding book about the things which 
this science considers, and this is divided into three parts. First, he answers the question 
whether this science considers substances and accidents together, and whether it considers all 
substances. Second (548), he answers the question whether it belongs to this science to 
consider all of the following: one and many, same and different, opposites, contraries, and so 
forth ("Now although"). Third (588), he answers the question whether it belongs to this 
science to consider the principles of demonstration ("Moreover, it is necessary"). 

In regard to the first he does three things. First, he shows that it is the office of this science to 
consider both substances and accidents. Second (546), he shows that this science is chiefly 
concerned with substances ("But in every respect"). Third (547), he shows that it pertains to 
this science to consider all substances ("Now of every"). 

In regard to the first part he uses this kind of argument: those things which have one term 
predicated of them in common, not univocally but analogously, belong to the consideration of 
one science. But the term being is thus predicated of all beings. Therefore all beings, i.e., both 
substances and accidents, belong to the consideration of one science which considers being as 
being. 

535. Now in this argument he gives, first (535), the minor premise; second (544), the major 
premise ("Therefore, just as"); and third (545), the conclusion ("It is evident, then"). 

He accordingly says, first, that the term being, or what is, has several meanings. But it must 
be noted that a term is predicated of different things in various senses. Sometimes it is 
predicated of them according to a meaning which is entirely the same, and then it is said to be 
predicated of them univocally, as animal is predicated of a horse and of an ox. Sometimes it is 
predicated of them according to meanings which are entirely different, and then it is said to be 
predicated of them equivocally, as dog is predicated of a star and of an animal. And 
sometimes it is predicated of them according to meanings which are partly different and 
partly not (different inasmuch as they imply different relationships, and the same inasmuch as 
these different relationships are referred to one and the same thing), and then it is said "to be 
predicated analogously," i.e., proportionally, according as each one by its own relationship is 
referred to that one same thing. 

536. It must also be noted that the one thing to which the different relationships are referred in 
the case of analogical things is numerically one and not just one in meaning, which is the kind 


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of oneness designated by a univocal term. Hence he says that, although the term being has 
several senses, still it is not predicated equivocally but in reference to one thing; not to one 
thing which is one merely in meaning, but to one which is one as a single definite nature. This 
is evident in the examples given in the text. 

537. First, he gives the example of many things being related to one thing as an end. This is 
clear in the case of the term healthy or healthful. For the term healthy is not predicated 
univocally of food, medicine, urine and an animal; because the concept healthy as applied to 
food means something that preserves health; and as applied to medicine it means something 
that causes health; and as applied to urine it means something that is a sign of health; and as 
applied to an animal it means something that is the recipient or subject of health. Hence every 
use of the term healthy refers to one and the same health; for it is the same health which the 
animal receives, which urine is a sign of, which medicine causes, and which food preserves. 

538. Second, he gives the example of many things being related to one thing as an efficient 
principle. For one thing is called medical because it possesses the art of medicine, as the 
skilled physician. Another is called medical because it is naturally disposed to have the art of 
medicine, as men who are so disposed that they may acquire the art of medicine easily (and 
according to this some men can engage in medical activities as a result of a peculiar natural 
constitution). And another is called medical or medicinal because it is necessary for healing, 
as the instruments which physicians use can be called medical. The same thing is also true of 
the things called medicines, which physicians use in restoring health. Other terms which 
resemble these in having many senses can be taken in a similar way. 

539. And just as the above-mentioned terms have many senses, so also does the term being. 
Yet every being is called such in relation to one first thing, and this first thing is not an end or 
an efficient cause, as is the case in the foregoing examples, but a subject. 

For some things are called beings, or are said to be, because they have being of themselves, as 
substances, which are called beings in the primary and proper sense. Others are called beings 
because they are affections or properties of substances, as the proper accidents of any 
substance. Others are called beings because they are processes toward substance, as 
generation and motion. And others are called beings because they are corruptions of 
substances; for corruption is the process toward non-being just as generation is the process 
toward substance. And since corruption terminates in privation just as generation terminates 
in form, the very privations of substantial forms are fittingly called beings. Again, certain 
qualities or certain accidents are called beings because they are productive or generative 
principles of substances or of those things which are related to substance according to one of 
the foregoing relationships or any other relationship. 

And similarly the negations of those things which are related to substances, or even substance 
itself, are also called beings. Hence we say that non-being is non-being. But this would not be 
possible unless a negation possessed being in some way. 

540. But it must be noted that the above-mentioned modes of being can be reduced to four. 

(1) For one of them, which is the most imperfect, i.e., negation and privation, exists only in 
the mind. We say that these exist in the mind because the mind busies itself with them as 
kinds of being while it affirms or denies something about them. In what respect negation and 
privation differ will be treated below (564). 


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541. (2) There is another mode of being inasmuch as generation and corruption are called 
beings, and this mode by reason of its imperfection comes close to the one given above. For 
generation and corruption have some admixture of privation and negation, because motion is 
an imperfect kind of actuality, as is stated in the Physics, Book III. 

542. (3) The third mode of being admits of no admixture of non-being, yet it is still an 
imperfect kind of being, because it does not exist of itself but in something else, for example, 
qualities and quantities and the properties of substances. 

543. (4) The fourth mode of being is the one which is most perfect, namely, what has being in 
reality without any admixture of privation, and has firm and solid being inasmuch as it exists 
of itself. This is the mode of being which substances have. Now all the others are reduced to 
this as the primary and principal mode of being; for qualities and quantities are said to be 
inasmuch as they exist in substances; and motions and generations are said to be inasmuch as 
they are processes tending toward substance or toward some of the foregoing; and negations 
and privations are said to be inasmuch as they remove some part of the preceding three. 

544. Therefore, just as (298). 

Here he gives the major premise of the first argument. He says that it is the office of one 
science to study not only those things which are referred "to one thing," i.e., to one common 
notion, but also those which are referred to one nature according to different relationships. 
And the reason for this is that the thing to which they are referred is one; just as it is clear that 
one science, medicine, considers all health-giving things. The same thing holds true of other 
things which are spoken of in the same way. 

545. It is evident (299). 

Then he draws his intended conclusion. This is evident of itself. 

546. But in every (299a). 

Then he shows that this science, even though it considers all beings, is chiefly concerned with 
substances. He uses the following argument. Every science which deals with many things that 
are referred to one primary thing is properly and principally concerned with that primary 
thing on which other things depend for their being and from which they derive their name; 
and this is true in every case. But substance is the primary kind of being. Hence the 
philosopher who considers all beings ought to consider primarily and chiefly the principles 
and causes of substances. Therefore his consideration extends primarily and chiefly to 
substances. 

547. Now of every (300). 

Then he shows by the following argument that it is the business of the first philosopher to 
consider all substances. There is one sense and one science of all things belonging to one 
class; for example, sight is concerned with all colors, and grammar with all words. Therefore, 
if all beings somehow belong to one class, all species of being must belong to the 
consideration of one science which is a general science, and different species of being must 
belong to the different species of that science. He says this because it is not necessary for one 
science to consider all the species of one genus according to the special notes of every single 
species, but only inasmuch as they agree generically. But according to their specific notes the 


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different species of one genus belong to the special sciences, as happens in the present case. 
For inasmuch as all substances are beings or substances, they belong to the consideration of 
this science; but inasmuch as they are a particular kind of substance, as a lion or an ox, they 
belong to the special sciences. 


LESSON 2 

This Science Considers Being and Unity. The Parts of Philosophy Based on the Divisions of 
Being and Unity 

ARISTOTLE'S TEXT Chapter 2: 1003b 22-1004a 9 

301. Now although being and unity are the same and are a single nature in the sense that they 
are associated like principle and cause, they are not the same in the sense that they are 
expressed by a single concept. Yet it makes no difference even if we consider them to be the 
same; in fact this will rather support our undertaking. 

302. For one man and human being and man are the same thing; and nothing different is 
expressed by repeating the terms when we say, "This is a human being, a man, and one man." 
And it is evident that they are not separated either in generation or in corruption. The same 
holds true of what is one. Hence it is evident that any addition to these expresses the same 
thing, and that unity is nothing else than being. 

303. Further, the substance of each thing is one in no accidental way; and similarly it is 
something that is. 

304. Hence there are as many species of being as there are of unity, of which it is the office of 
the same general science to treat. I mean, for example, sameness and likeness and other such 
attributes. And almost all contraries may be referred to this starting point. But these have been 
studied by us in our selection, i.e., in our explanation or treatment, of contraries. 

305. And there are just as many parts of philosophy as there are substances, so that there must 
be a first philosophy and one which is next in order to it. For being and unity are things which 
straightway have genera; and for this reason the sciences will correspond to these. For the 
term philosopher is used like the term mathematician; for mathematics too has parts, and 
there is a first and a second science and then others " following these among the mathematical 
sciences. 

COMMENTARY 

Metaphysics also treats of "being-one ". 

548. Here he proceeds to show that the study of common attributes such as one and many and 
same and different belongs to the consideration of one and the same science; and in regard to 
this he does two things. First, he shows that this is true of each attribute taken separately by 
arguing from proper or specific principles. Second (570), he shows that this is true of all 
attributes taken together by arguing from common principles. 


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In regard to the first he does two things. First, he shows that the philosopher ought to 
investigate all these attributes. Second (568), he tells us how to investigate them. 

In regard to the first he does two things. First, he shows that it is the office of this science to 
consider unity and its species. Second (564), he shows that it is the office of one and the same 
science to consider all opposites. 

In regard to the first he does two things. First, he shows that it is the office of this science to 
consider unity. Second (561), he shows that it also,belongs to it to examine the species of 
unity. 

He therefore says, first, that being and unity are the same and are a single nature. He says this 
because some things are numerically the same which are not a single nature but different 
natures, for example, Socrates, this white thing, and this musician. Now the terms one and 
being do not signify different natures but a single nature. But things can be one in two ways: 
(1) for some things are one which are associated as interchangeable things, like principle and 
cause; and (2) some are interchangeable not only in the sense that they are one and the same 
numerically [or in subject] but also in the sense that they are one and the same conceptually, 
like garment and clothing. 

549. Now the terms one and being signify one nature according to different concepts, and 
therefore they are like the terms principle and cause, and not like the terms tunic and garment, 
which are wholly synonymous. — Yet it makes no difference to his thesis if we consider them 
to be used in the same sense, as those things which are one both numerically and 
conceptually. In fact this will "rather support our undertaking," i.e., it will serve his purpose 
better; for he intends to prove that unity and being belong to the same study, and that the 
species of the one correspond to those of the other. The proof of this would be clearer if unity 
and being were the same both numerically and conceptually rather than just numerically and 
not conceptually. 

550. He proves that they are the same numerically by using two arguments. He gives the first 
where he says, "For one man," and it runs as follows. Any two things which when added to 
some third thing cause no difference are wholly the same. But when one and being are added 
to man or to anything at all, they cause no difference. Therefore they are wholly the same. 
The truth of the minor premise is evident; for it is the same thing to say "man" and "one 
man." And similarly it is the same thing to say "human being" and "the thing that is man;" 
and nothing different is expressed when in speaking we repeat the terms, saying, "This is a 
human being, a man, and one man." He proves this as follows. 

55 1 . It is the same thing for man and the thing that is man to be generated and corrupted. This 
is evident from the fact that generation is a process toward being, and corruption a change 
from being to non-being. Hence a man is never generated without a human being being 
generated, nor is a man ever corrupted without a human being being corrupted; and those 
things which are generated and corrupted together are themselves one and the same. 

552. And just as it has been said that being and man are not separated either in generation or 
in corruption, so too this is evident of what is one; for when a man is generated, one man is 
generated, and when a man is corrupted, one man is also corrupted. It is clear, then, that the 
apposition of these [i.e., of one or being to man] expresses the same thing, and that just 
because the term one or being is added to man it is not to be understood that some nature is 
added to man. And from this it is clearly apparent that unity does not differ from being, 


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because any two things which are identical with some third thing are identical with each 
other. 

553. It is also evident from the foregoing argument that unity and being are the same 
numerically but differ conceptually; for if this were not the case they would be wholly 
synonymous, and then it would be nonsense to say, "a human being," and "one man." For it 
must be borne in mind that the term man is derived from the quiddity or the nature of man, 
and the term thing from the quiddity only; but the term being is derived from the act of being, 
and the term one from order or lack of division; for what is one is an undivided being. Now 
what has an essence, and a quiddity by reason of that essence, and what is undivided in itself, 
are the same. Hence these three — thing, being, and one — signify absolutely the same thing 
but according to different concepts. 

554. Further, the substance (303). 

Then he gives the second argument, which has to do with sameness or identity of subject. 
This argument is as follows. Any two attributes which are predicated essentially and not 
accidentally of the substance of each thing are the same in subject, or numerically. But unity 
and being are such that they are predicated essentially and not accidentally of the substance of 
each thing; for the substance of a thing is one in itself and not accidentally. Therefore the 
terms being and one signify the same thing in subject. 

555. That the terms being and one are predicated essentially and not accidentally of the 
substance of each thing can be proved as follows. If being and one were predicated of the 
substance of each thing by reason of something added to it [i.e., accidentally], being would 
have to be predicated also of the thing added, because anything at all is one and a being. But 
then there would be the question whether being is predicated of this thing (the one added) 
either essentially or by reason of some other thing that is added to it in turn. And if the latter 
were the case, then the same question would arise once again regarding the last thing added, 
and so on to infinity. But this is impossible. Hence the first position must be held, namely, 
that a thing's substance is one and a being of itself and not by reason of something added to it. 

556. But it must be noted that Avicenna felt differently about this; for he said that the terms 
being and one do not signify a thing's substance but something added to it. He said this of 
being because, in the case of anything that derives its existence from something else, the 
existence of such a thing must differ from its substance or essence. But the term being 
signifies existence itself. Hence it seems that being, or existence is something added to a 
thing's essence. 

557. He spoke in the same way of one, because he thought that the one which is 
interchangeable with being and the one which is the principle of number are the same. And 
the one which is the principle of number must signify a reality added to the substance, 
otherwise number, since it is composed of ones, would not be a species of quantity, which is 
an accident added to substance. He said that this kind of one is interchangeable with being, 
not in the sense that it signifies the very substance of a thing or being, but in the sense that it 
signifies an accident belonging to every being, just as the ability to laugh belongs to every 
man. 

558. But in regard to the first point he does not seem to be right; for even though a thing's 
existence is (+) other than its essence, it should not be understood to be something added to 
its essence after the manner of an (~) accident, but (+) something established, as it were, by 


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the principles of the essence. Hence the term being, which is applied to a thing by reason of 
its very existence, designates the same thing as the term which is applied to it by reason of its 
essence. [Existence is later clarified as the act of essence.] 

559. Nor does it seem to be true that the one or unity which is interchangeable with being and 
that which is the principle of number are the same; for nothing that pertains to some special 
class of being seems to be characteristic of all beings. Hence the unity which is limited to a 
special class of being — discrete quantity — does not seem to be interchangeable with universal 
being. For, if unity is a proper and essential accident of being, it must be caused by the 
principles of being as being, just as any proper accident is caused by the principles of its 
subject. But it is not reasonable that something having a particular mode of being should be 
adequately accounted for by the common principles of being as being. It cannot be true, then, 
that something which belongs to a definite genus and species is an accident of every being. 

560. Therefore the kind of unity which is the principle of number differs from that which is 
interchangeable with being; for the unity which is interchangeable with being signifies being 
itself, adding to it the notion of undividedness, which, since it is a negation or a privation, 
does not posit any reality added to being. Thus unity differs from being in no way 
numerically but only conceptually; for a negation or a privation is not a real being but a being 
of reason, as has been stated (540). 

However, the kind of unity which is the principle of number adds to substance the note of a 
measure, which is a special property of quantity and is found first in the unit. And it is 
described as the privation or negation of division which pertains to continuous quantity; for 
number is produced by dividing the continuous. Hence number belongs to mathematical 
science, whose subject cannot exist apart from sensible matter but can be considered apart 
from sensible matter. But this would not be so if the kind of unity which is the principle of 
number were separate from matter in being and existed among the immaterial substances, as 
is true of the kind of unity which is interchangeable with being. 

561. Hence there are (304). 

Then he concludes that it is the business of the philosopher to consider the parts of unity, just 
as it is to consider the parts of being. First, he proves this; and second (563), he shows that 
there are different parts of philosophy corresponding to the different parts of being and unity. 

He says, first, that since being and unity signify the same thing, and the species of things that 
are the same are themselves the same, there must be as many species of being as there are of 
unity, and they must correspond to each other. For just as the parts of being are substance, 
quantity, quality, and so on, in a similar way the parts of unity are sameness, equality and 
likeness. For things are the same when they are one in substance, equal when they are one in 
quantity, and like when they are one in quality. And the other parts of unity could be taken 
from the other parts of being, if they were given names. And just as it is the office of one 
science, philosophy, to consider all parts of being, in a similar way it is the office of this same 
science to consider all parts of unity, i.e., sameness, likeness and so forth. And to this 
"starting point," i.e., unity, "almost" all contraries may be referred. 

562. He adds this qualification because in some cases this point is not so evident. Yet it must 
be true; for since one member of every pair of contraries involves privation, they must be 
referred back to certain primary privatives, among which unity is the most basic. 


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And plurality, which stems from unity, is the cause of otherness, difference and contrariety, as 
will be stated below. He says that this has been treated "in our selection," or extract, "of 
contraries," i.e., a treatise which is the part selected to deal with contraries, namely, Book X 
(2000-21) of this work. 

563. And there are (305). 

Here he shows that the parts of philosophy are distinguished in reference to the parts of being 
and unity. He says that there are as many parts of philosophy as there are parts of substance, 
of which being and unity chiefly are predicated, and of which it is the principal intention or 
aim of this science to treat. 

And because the parts of substance are related to each other in a certain order, for immaterial 
substance is naturally prior to sensible substance, then among the parts of philosophy there 
must be a first part. (1) Now that part which is concerned with sensible substance is first in 
the order of instruction, because any branch of learning must start with things which are better 
known to us. He treats of this part in Books VII (1300) and VIII of this work. (2) But that part 
which has to do with immaterial substance is prior both in dignity and in the aim of this 
science. This part is treated in Book XII (2488) of this work. 

Yet whatever parts are first must be continuous with the others, because all parts have unity 
and being as their genus. Hence all parts of this science are united in the study of being and 
unity, although they are about different parts of substance. Thus it is one science inasmuch as 
the foregoing parts are things which correspond to "these,"i.e., to unity and being, as common 
attributes of substance. In this respect the philosopher resembles the mathematician; for 
mathematical science has different parts, one of which is primary, as arithmetic, another 
secondary, as geometry, and others following these in order, as optics, astronomy and music. 


LESSON 3 

The Same Science Considers Unity and Plurality and All Opposites. The Method of Treating 
These 

ARISTOTLE'S TEXT Chapter 2: 1004a 9-1004a 34 

306. Now since it is the office of a single science to study opposites, and plurality is the 
opposite of unity, it is also the office of a single science to study negation and privation, 
because in both cases we are studying the unity of which there is negation or privation. And 
this (negation or privation) is what is stated either absolutely because an attribute is not 
present in a thing or (not absolutely) because it is not present in some determinate class. 
Therefore this difference is present in unity over and above what is implied in negation; for 
negation is the absence of the thing in question. But in the case of privation there is an 
underlying subject of which the privation is predicated. 

307. But plurality is the opposite of unity. Hence the opposites of the abovementioned 
concepts, otherness, unlikeness, and inequality, and any others which are referred to plurality 
or unity, must come within the scope of the science mentioned above. And contrariety is one 
of these; for contrariety is a kind of difference, and difference is a kind of otherness. 


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308. Hence, since the term one is used in many senses, the terms designating the foregoing 
opposites will also be used in many senses. Yet it is the business of one science to know them 
all. For even if some term is used in many senses, it does not therefore follow that it belongs 
to another science. Hence if terms are not used with one meaning, and their concepts are not 
referred to one thing, then it is the office of a different science to study them. But since all 
things are referred to some primary thing, as all things which are one are referred to a primary 
one, the same thing must hold true of sameness, otherness, and the contraries. It is necessary, 
then to distinguish all the senses in which each term is used and then refer them back to the 
primary thing signified in each of the predicates in question to see how each is related to it. 
For one thing is given a particular predicate because it possesses it, another because it 
produces it, and others in other ways. 

309. Hence it is evident, as has been stated in our problems, that it is the office of a single 
science to give an account of these predicates as well as of substance; and this was one of the 
problems (181 :C 346; 202:C 393). 

COMMENTARY 

It also considers "one-many", "negation-privation" etc. 

564. Here he shows that it is the office of this science to consider opposites; and in regard to 
this he does two things. First, he shows that it is the office of this science to consider privation 
and negation; and second (567), to consider contraries ("But plurality"). 

He accordingly says (306) that, since it pertains to one science to consider opposites (for 
example, it belongs to medicine to consider health and sickness, and to grammar to consider 
agreement and disagreement), and since plurality is the opposite of unity, the study of 
privation and negation must belong to that science which deals with unity and plurality. For 
the consideration "of both" involves unity; that is, the study of unity, whose concept entails 
negation and privation, depends on both of these. For, as has been said above (553), what is 
one is an undivided being, and division relates to plurality, which is the opposite of unity. 
Hence the study of negation and privation belongs to that science whose business it is to 
consider unity. 

565. Now there are two kinds of negation: (1) simple negation, by which one thing is said 
absolutely not to be present in something else, and (2) negation in a genus, by which 
something is denied of something else, not absolutely, but within the limits of some 
determinate genus. For example, not everything that does not have sight is said absolutely to 
be blind, but something within the genus of an animal which is naturally fitted to have sight. 

And this difference is present in unity over and above "what is implied in negation"; i.e., it is 
something by which it differs from negation, because negation expresses only the absence of 
something, namely, what it removes, without stating a determinate subject. (1) Hence simple 
negation can be verified both of a non43eing, which is not naturally fitted to have something 
affirmed of it, and of a being which is naturally fitted to have something affirmed of it and 
does not. For unseeing can be predicated both of a chimera and of a stone and of a man. (2) 
But in the case of privation there is a determinate nature or substance of which the privation is 
predicated; for not everything that does not have sight can be said to be blind, but only that 
which is naturally fitted to have sight. Thus since the negation which is included in the 
concept of unity is a negation in a subject (otherwise a non43eing could be called one), it is 
evident that unity differs from simple negation and rather resembles the nature of privation, as 


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is stated below in Book X (2069) of this work. 

566. But it must be noted that, although unity includes an implied privation, it must not be 
said to include (~) the privation of plurality; for, since a privation is subsequent in nature to 
the thing of which it is the privation, it would follow that unity would be subsequent in nature 
to plurality. And it would also follow that plurality would be given in the definition of unity; 
for a privation can be defined only by its opposite. For example, if someone were to ask what 
blindness is, we would answer that it is the privation of sight. Hence, since unity is given in 
the definition of plurality (for plurality is an aggregate of units), it would follow that there 
would be circularity in definitions. (+) Hence it must be said that unity includes the privation 
of division, although not (~) the kind of division that belongs to quantity; for this kind of 
division is limited to one particular class of being and cannot be included in the definition of 
unity. (+) But the unity which is interchangeable with being implies the privation of formal 
division, which comes about through opposites, and whose primary root is the opposition 
between affirmation and negation. For those things are divided from each other which are of 
such a kind that one is not the other. Therefore being itself is understood first, and then 
non-being, and then division, and then the kind of unity which is the privation of division, and 
then plurality, whose concept includes the notion of division just as the concept of unity 
includes the notion of undividedness. However, some of the things that have been 
distinguished in the foregoing way can be said to include the notion of plurality only if the 
notion of unity is first attributed to each of the things distinguished. 

567. But plurality (307). 

Here he shows that it is the business of the philosopher to consider contraries, or opposites; 
for plurality is the opposite of unity, as has been said (564), and it is the office of one science 
to consider opposites. Hence, since this science considers unity, sameness, likeness and 
equality, it must also consider their opposites, plurality, otherness or diversity, unlikeness and 
inequality, and all other attributes which are reduced to these or even to unity and plurality. 
And contrariety is one of these; for contrariety is a kind of difference, namely, of things 
differing in the same genus. But difference is a kind of otherness or diversity, as is said in 
Book X (2017). Therefore contrariety belongs to the consideration of this science. 

568. Hence, since (308). 

Then he deals with the method by which the philosopher ought to establish these things. He 
says that, since all of the above-mentioned opposites are derived from unity, and the term one 
is used in many senses, all of the terms designating these must also be used in many senses, 
i.e., same, other, and so on. Yet even though all of these are used in many senses, it is still the 
work of one science, philosophy, to know the things signified by each of these terms. For if 
some term is used in many senses, it does not therefore follow that it belongs to another or 
different science. For if the different things signified are not referred to "with one meaning," 
or according to one concept, i.e., univocally, or are not referred to one thing in different ways, 
as in the case of analogous things, then it follows that it is the office of another, i.e., of a 
different, science, to consider them; or at least it is the office of one science accidentally, just 
as astronomy considers a star in the heavens, i.e., the dog star, and natural science considers a 
dog-fish and a dog. But all of these are referred to one starting point. For things signified by 
the term one, even though diverse, are referred back to a primary thing signified as one; and 
we must also speak in the same way of the terms same, other, contrary, and others of this 
kind. 


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Regarding each of these terms, then, the philosopher should do two things. (1) First, he 
should distinguish the many senses in which each may be used; and (2) second, he should 
determine regarding "each of the predicates," i.e., each of the names predicated of many 
things, to what primary thing it is referred. For example, he should state what the first thing 
signified by the term same or other is, and how all the rest are referred to it; one inasmuch as 
it possesses it, another inasmuch as it produces it, or in other ways of this kind. 

569. Hence it is evident (309). 

He draws his conclusion from what has been said, namely, that it belongs to this science to 
reason about those common predicates and about substance; and this was one of the problems 
investigated in the questions treated dialectically in Book III (393). 


LESSON 4 

First Philosophy Considers All Contraries. Its Distinction from Logic 
ARISTOTLE'S TEXT Chapter 2: 1004a 34-1005a 18 

310. And it is also evident that it is the function of the philosopher to be able to study all 
things. For if it is not the function of the philosopher, who is it that will investigate whether 
Socrates and Socrates sitting are the same person, or whether one thing has one contrary, or 
what a contrary is, or how many meanings it has? And the same applies to other questions of 
this kind. Therefore, since these same things are the essential properties of unity as unity and 
of being as being, but not as numbers or lines or fire, evidently it is the office of this science 
to know both the quiddities of these and their accidents. Therefore those who have been 
studying these things do not err by being unphilosophical, but because substance, to which 
they pay no attention, is first. Now there are properties of number as number, for example, 
oddness and evenness, commensurability and equality, excess and defect, and these belong to 
numbers either in themselves or in relation to one another. And similarly there are properties 
of the solid, and of what is changeable and what is unchangeable, and of what is heavy and 
what is light. And in a similar fashion there are properties of being as being; and these are the 
ones about which the philosopher has to investigate the truth. 

311. An indication of this is the following. Dialecticians and sophists assume the same guise 
as the philosopher, for sophistry is apparent wisdom, and dialecticians dispute about all 
things, and being is common to all things. But evidently they dispute about these matters 
because they are common to philosophy. For sophistry and dialectics are concerned with the 
same class of things as philosophy. 

312. But philosophy differs from the latter in the manner of its power, and from the former in 
the choice, i.e., selection, of a way of life. For dialectics is in search of knowledge of what the 
philosopher actually knows, and sophistry has the semblance of wisdom but is not really such. 

313. Further, one corresponding member of each pair of contraries is privative, and all 
contraries are referred to being and to non-being and to unity and to plurality; for example, 
rest pertains to unity and motion to plurality. 


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314. And almost all men admit that substance and beings are composed of contraries; for all 
say that principles are contraries. For some speak of the odd and even, others of the hot and 
cold, others of the limited and unlimited, and others of love and hate. 

315. And all the other contraries seem to be reducible to unity and plurality. Therefore let us 
take that reduction for granted. And all the principles which have to do with other things fall 
under unity and being as their genera. 

316. It is clear from these discussions, then, that it is the office of one science to study being 
as being. For all beings are either contraries or composed of contraries, and the principles of 
contraries are unity and plurality. And these belong to one science, whether they are used in 
one sense or not. And perhaps the truth is that they are not. Yet even if the term one is used in 
many senses, all will be referred to one primary sense; and the same is true of contraries. 
Hence, even if unity or being is not a universal and the same in all things or is something 
separate (as presumably it is not), still in some cases the thing will be referred to unity and in 
others it will be referred to what follows on unity. 

317. And for this reason it is not the province of geometry to examine what a contrary is, or 
what the perfect is, or what unity is, or what sameness or otherness is, but to assume them. 

318. It is evident, then, that it is the office of one science to study both being as being and the 
attributes which belong to being as being. And it is evident too that the same science studies 
not only substances but also their accidents, both those mentioned above, and prior and 
subsequent, genus and species, whole and part, and others such as these. 

COMMENTARY 

General reasons for that (difference between metaphysics and dialectics or sophistry). 

570. Here he uses arguments based on common principles to prove what the philosopher 
ought to consider regarding all of the foregoing attributes. First, he proves his thesis; and 
second (587), he introduces his intended conclusion ("It is evident"). 

In regard to the first part he does two things. First, he proves his thesis; and second (586), he 
draws a corollary from what has been said ("And for this reason"). 

He gives three arguments to prove his thesis. The second (572) begins where he says, "An 
indication of this"; and the third (578), at "Further, one corresponding." 

The first argument is as follows. All questions that can be raised must be answered by some 
science. But questions are raised about the common attributes mentioned above, for example, 
that raised about sameness and otherness: whether Socrates and Socrates sitting are the same; 
and that raised about contraries: whether one thing has one contrary, and how many meanings 
the term contrary has. Hence these questions must be answered by some science which 
considers sameness and contrariety and the other attributes mentioned above. 

571. That this is the job of the philosopher and of no one else he proves thus: that science 
whose office is to consider being as being is the one which must consider the first properties 
of being. But all of the above-mentioned attributes are proper accidents of unity and being as 
such. For number as number has properties, such as excess, equality, commensurability, and 
so on, some of which belong to a number taken absolutely, as even and odd, and some to one 


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number in relation to another, as equality. And even substance has proper attributes, "as the 
resistant," or body, and others of this kind. And in a similar way being as being has certain 
properties, which are the common attributes mentioned above; and therefore the study of 
them belongs to the philosopher. Hence those dealing with philosophy have not erred in their 
treatment of these things "by being unphilosophical," i.e., by considering them in a way that 
does not pertain to the investigations of philosophy, but because in treating them they pay no 
attention to substance, as though they were completely unmindful of it despite the fact that it 
is the first thing which the philosopher ought to consider. 

572. An indication (311). 

Then he gives a second argument to prove the same point. This argument employs an 
example and runs thus: dialecticians and sophists assume the same guise as the philosopher 
inasmuch as they resemble him in some respect. But the dialectician and sophist dispute about 
the above-mentioned attributes. Therefore the philosopher should also consider them. In 
support of his first premise he shows how dialectics and sophistry resemble philosophy and 
how they differ from it. 

573. Dialectics resembles philosophy in that it is also the office of the dialectician to consider 
all things. But this could not be the case unless he considered all things insofar as they agree 
in some one respect; because each science has one subject, and each art has one matter on 
which it operates. Therefore, since all things agree only in being, evidently the subject matter 
of dialectics is being and those attributes which belong to being; and this is what the 
philosopher also investigates. And sophistry likewise resembles philosophy; for sophistry has 
"the semblance of wisdom," or is apparent wisdom, without being wisdom. Now anything 
that takes on the appearance of something else must resemble it in some way. Therefore the 
philosopher, the dialectician and the sophist must consider the same thing. 

574. Yet they differ from each other. The philosopher differs from the dialectician in power, 
because the consideration of the philosopher is more efficacious than that of the dialectician. 
For the philosopher proceeds demonstratively in dealing with the common attributes 
mentioned above, and thus it is proper to him to have scientific knowledge of these attributes. 
And he actually knows them with certitude, for certain or scientific knowledge is the effect of 
demonstration. The dialectician, however, proceeds to treat all of the above-mentioned 
common attributes from probable premises, and thus he does not acquire scientific knowledge 
of them but a kind of opinion. The reason for this difference is that there are two kinds of 
beings: beings of reason and real beings. The expression being of reason is applied properly 
to those notions which reason derives from the objects it considers, for example, the notions 
of genus, species and the like, which are not found in reality but are a natural result of the 
consideration of reason. And this kind of being, i.e., being of reason, constitutes the proper 
subject of logic. But intellectual conceptions of this kind are equal in extension to real beings, 
because all real beings fall under the consideration of reason. Hence the subject of logic 
extends to all things to which the expression real being is applied. His conclusion is, then, that 
the subject of logic is equal in extension to the subject of philosophy, which is real being. 

Now the philosopher proceeds from the principles of this kind of being to prove the things 
that have to be considered about the common accidents of this kind of being. But the 
dialectician proceeds to consider them from the conceptions of reason, which are extrinsic to 
reality. Hence it is said that dialectics is in search of knowledge, because in searching it is 
proper to proceed from extrinsic principles. 


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575. But the philosopher differs from the sophist "in the choice," i.e., in the selection or 
willing, or in the desire, of a way of life. For the philosopher and sophist direct their life and 
actions to different things. The philosopher directs his to knowing the truth, whereas the 
sophist directs his so as to appear to know what he does not. 

576. Now although it is said that philosophy is scientific knowledge, and that dialectics and 
sophistry are not, this still does not do away with the possibility of dialectics and sophistry 
being sciences. For dialectics can be considered both from the viewpoint of theory and from 
that of practice. (1) From the viewpoint of theory it studies these conceptions and establishes 
the method by which one proceeds from them to demonstrate with probability the conclusions 
of the particular sciences; and it does this demonstratively, and to this extent it is a science. 
(2) But from the viewpoint of practice it makes use of the above method so as to reach certain 
probable conclusions in the particular sciences; and in this respect it falls short of the 
scientific method. 

The same must be said of sophistry, because from the viewpoint of theory it treats by means 
of necessary and demonstrative arguments the method of arguing to apparent truth. From the 
viewpoint of practice, however, it falls short of the process of true argumentation. 

577. But that part of logic which is said to be demonstrative is concerned only with theory, 
and the practical application of it belongs to philosophy and to the other particular sciences, 
which are concerned with real beings. This is because the practical aspect of the 
demonstrative part of logic consists in using the principles of things, from which proceeds 
demonstration (which properly belongs to the sciences that deal with real beings), and not in 
using the conceptions of logic. 

Thus it appears that some parts of logic are at the same time scientific, theoretical, and 
practical, as exploratory dialectics and sophistry; and one is concerned with theory and not 
practice, namely, demonstrative logic. 

578. Further, one corresponding (313). 

Then he gives the third argument in support of his thesis. It runs as follows: everything that is 
reducible to unity and being should be considered by the philosopher, whose function is to 
study unity and being. But all contraries are reducible to unity and being. Therefore all 
contraries belong to the consideration of the philosopher, whose function is to study unity and 
being. 

579. Then he proves that all contraries are reducible to unity and being. He does this, first, 
with regard to being; and he proceeds thus: of any two contraries which the philosophers 
posited as the principles of things, as is said in Book I (62:C 132), one contrary is always the 
correlative of the other and is related to it as its privation. This is clear from the fact that one 
of two contraries is always something imperfect when compared with the other, and thus 
implies some privation of the perfection of the other. But a privation is a kind of negation, as 
was stated above (306:C 564), and thus is a non-being. Hence it is clear that all contraries are 
reducible to being and non-being. 

580. He also shows by an example that all contraries are reducible to unity and plurality. For 
rest or repose is reducible to unity, since that is said to be at rest which is in the same 
condition now as it was before, as is stated in Book VI of the Physics. And motion is 
reducible to plurality, because whatever is in motion is in a different condition now than it 


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was before, and this implies plurality. 

581. And almost all (314). 

Then he uses another argument to show that contraries are reducible to being. Both the 
principles of things and the things composed of them belong to the same study. But the 
philosophers admit that contraries are the principles of being as being; for all say that beings 
and the substances of beings are composed of contraries, as was stated in Book I of the 
Physics and in the first book of this work (62:C 132). Yet while they agree on this point, that 
the principles of beings are contraries, still they differ as to the contraries which they give. 
For some give the even and odd, as the Pythagoreans; others the hot and cold, as Parmenides; 
others "the end" or terminus "and the unlimited," i.e., the finite and infinite, as did the same 
Pythagoreans (for they attributed limitedness and unlimitedness to the even and the odd, as is 
stated in Book I (59:C 124); and still others gave friendship and strife, as Empedocles. Hence 
it is clear that contraries are reducible to the study of being. 

582. And all the other (315). 

He says that the above-mentioned contraries are redudible not only to being but also to unity 
and plurality. This is evident. For oddness by reason of its indivisibility is affiliated with 
unity, and evenness by reason of its divisibility has a natural connection with plurality. Thus 
end or limit pertains to unity, which is the terminus of every process of resolution, and lack of 
limit pertains to plurality, which may be increased to infinity. Again, friendship also clearly 
pertains to unity, and strife to plurality. And heat pertains to unity inasmuch as it can unite 
homogeneous things, whereas cold pertains to plurality inasmuch as it can separate them. 
Further, not only these contraries are reducible in this way to unity and plurality, but so also 
are the others. Yet this "reduction," or introduction, to unity and plurality let us now accept or 
"take for granted," i.e., let us now assume it, because to examine each set of contraries would 
be a lengthy undertaking. 

583. Next he shows that all contraries are reducible to unity and being. For it is certain that all 
principles, inasmuch as they have to do "with other things" i.e., the things composed of them, 
fall under unity and being as their genera, not in the sense that they truly are genera, but in the 
sense that they bear some likeness to genera by reason of what they have in common. Hence, 
if all contraries are principles or things composed of principles, they must be reducible to 
unity and being.Thus it is clear that he shows that contraries are reducible to being for two 
reasons: first, because of the nature of privation, and second, by reason of the fact that 
contraries are principles. He shows that they are reducible to unity by giving an example and 
by using a process of reduction. Last, he shows that they are reducible to unity and being 
inasmuch as they have the character of genera. 

584. It is clear (316). 

Here he proves in a converse way that this science considers being because it considers the 
things mentioned above. His argument is this: all beings are reducible to contraries because 
they are either contraries or composed of contraries. And contraries are reducible to unity and 
plurality because unity and plurality are the principles of contraries. But unity and plurality 
belong to one science, philosophy. Therefore it is the office of this science to consider being 
as being. Yet it must be noted that all the contraries mentioned above fall under the 
consideration of one science whether they are used "in one sense," i.e., univocally, or not, as 
perhaps is the case. However, even if the term one is used in many senses, all the others, i.e., 


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all the other senses, are reducible to one primary sense. Hence, even if unity or being is not 
one universal, like a genus, as was stated above (whether a universal is said to be a one-in-all, 
as we maintain, or something separate from things, as Plato thought, and as is presumably not 
the case), still each is used in a primary and a secondary sense. And the same holds true in the 
case of other terms, for some senses are referred to one primary sense, and others are 
secondary with respect to that primary sense. An adverb designating uncertainty is used 
inasmuch as we are now assuming things that will be proved below. 

585. But nevertheless it must be borne in mind that the statement which he made, that all 
beings are either contraries or composed of contraries, he did not give as his own opinion but 
as one which he took from the ancient philosophers; for unchangeable beings are not 
contraries or composed of contraries. And this is why Plato did not posit any contrariety in 
the unchangeable sensible substances; for he attributed unity to form and contrariety to 
matter. But the ancient philosophers claimed that only sensible substances exist and that these 
must contain contrariety inasmuch as they are changeable. 

586. And for this reason (317) 

Then he draws a corollary from what has been said. He says that it is not the province of 
geometry to investigate the foregoing things, which are accidents of being as being, i.e., to 
investigate what a contrary is, or what the perfect is, and so on. But if a geometer were to 
consider them, he would "assume them," i.e., presuppose their truth, inasmuch as he would 
take them over from some prior philosopher from whom he accepts them insofar as they are 
necessary for his own subject matter. What is said about geometry must be understood to 
apply also in the case of any other particular science. 

587. It is evident (318). 

He now summarizes the points established above. He says that obviously the consideration of 
being as being and the attributes which belong to it of itself pertain to one science. Thus it is 
clear that that science considers not only substances but also accidents since being is 
predicated of both. And it considers the things which have been discussed, namely, sameness 
and otherness, likeness and unlikeness, equality and inequality, privation and negation, and 
contraries-which we said above are the proper accidents of being. And it considers not only 
those things which fall under the consideration of this science, about which demonstration 
was made individually by means of arguments based on proper principles, but it in like 
manner also considers prior and subsequent, genus and species, whole and part, and other 
things of this kind, because these too are accidents of being as being. 


LESSON 5 

Answers to Questions Raised in Book III about Principles of Demonstration 
ARISTOTLE'S TEXT Chapter 3: 1005a 19-1005b 8 

319. Moreover, it is necessary to state whether it is the office of one science or of different 
sciences to inquire about those principles which are called axioms in mathematics, and about 
substance. 


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320. Now it is evident that it is the office of one science — that of the philosopher — to 
investigate these. 

321. For these principles apply to all beings and not to some class distinct from the others. 
And all men employ them, because they pertain to being as being; for each class is being. But 
they employ them just so far as to satisfy their needs, i.e., so far as the class contains the 
things about which they form demonstrations. Hence, since it is evident that these principles 
pertain to all things inasmuch as they are beings (for this is what they have in common), the 
investigation of them belongs to him who considers being as being. 

322. Hence no one who is making a special inquiry attempts to say anything about their truth 
or falsity, neither the geometer nor the arithmetician. 

323. However, some of the philosophers of nature have done this, and with reason; for they 
thought that they alone were inquiring about the whole of nature and about being. But since 
there is one kind of thinker who is superior to the philosopher of nature (for nature is only one 
class of being), the investigation of these principles will belong to him who studies the 
universal and deals with first substance. The philosophy of nature is a kind of wisdom, but it 
is not the first. 

324. And whatever certain ones of 1 those who speak about the truth attempt to say 
concerning the way in which it must be accepted, they do this through ignorance of analytics. 
For they must know these principles in order to attain scientific knowledge and not be seeking 
them when they are learning a science. 

325. It is evident, then, that it is also the business of the philosopher, i.e., of him who 
investigates all substance insofar as its nature permits, to investigate all syllogistic principles. 

COMMENTARY 

This science considers the first principles of demonstration. 

588. Here he answers another question raised in Book III (387): whether it belongs to this 
science to consider the first principles of demonstration. This is divided into two parts. In the 
first he shows that it belongs to this science to make a general study of all these principles; 
and in the second (596) he shows that it also belongs to it to make a special study of the first 
of these principles ("And it is fitting"). 

In regard to the first he does three things. First, he raises the question whether it belongs to 
one or to different sciences to consider substance and the principles which are called axioms 
in the mathematical sciences. He assigns these principles more to the mathematical sciences 
because such sciences have more certain demonstrations and use these self-evident principles 
in a more manifest way inasmuch as they refer all of their demonstrations to them. 

589. Now it is evident (320). 

Second, he answers this question by saying that a single science investigates both of the 
foregoing things, and that this is the philosophy with which we are now concerned. 

590. For these principles (321). 


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Third, he proves his proposed answer, and in regard to this he does two things. First, he 
proves it. Second (595), he introduces his main conclusion ("It is evident"). 

Now he proves his proposed answer in two ways. He does this, first, by an argument; and 
second (592), by an example ("Hence no one"). 

The argument is as follows: whatever principles pertain to all beings, and not just to one class 
of beings distinct from the others, belong to the consideration of the philosopher. But the 
above-mentioned principles are of this kind. Therefore they belong to the consideration of the 
philosopher. He proves the minor premise as follows. Those principles which all sciences use 
pertain to being as being. But first principles are principles of this kind. Therefore they 
pertain to being as being. 

591. The reason which he gives for saying that all sciences use these principles is that the 
subject genus of each science has being predicated of it. Now the particular sciences do not 
use the foregoing principles insofar as they are common principles, i.e., as extending to all 
beings, but insofar as they have need of them; that is, insofar as they extend to the things 
contained in the class of beings which constitutes the subject of a particular science about 
which it makes demonstrations. For example, the philosophy of nature uses them insofar as 
they extend to changeable beings and no further. 

592. Hence no one (322). 

Then he proves what he had said by using an example. First, he introduces the proof; and 
second (593), he rejects a false notion held by some men ("However, some"). 

He accordingly says, first, that no one whose chief intention is to hand down scientific 
knowledge of some particular being has attempted to say anything about the truth or falsity of 
first principles. Neither the geometer nor the arithmetician does this even though they make 
the greatest use of these principles, as was said above (588). Hence it is evident that the 
investigation of these principles belongs to this science. 

593. However, some (323). 

Here he rejects the false notion held by some men, and in regard to this he does two things. 
First, he rejects the false notion of those who occupied themselves with these principles even 
though they did not concern them. Second, (594), he rejects the false notion of those who 
wanted to deal with these principles in a different way than they should be dealt with. 

He accordingly says, first, that even though none of the particular sciences ought to deal with 
the above-mentioned principles, nevertheless some of the natural philosophers have dealt with 
them; and they did so not without reason. For the ancients did not think that there was any 
substance besides the changeable corporeal substance with which the philosophy of nature is 
concerned. Hence they believed that they alone established the truth about the whole of nature 
and therefore about being, and thus about first principles, which must be considered along 
with being. But this is false, because there is still a science which is superior to the science of 
nature. For nature itself, i.e., natural being, which has its own principle of motion, constitutes 
in itself one class of universal being. 

But not every being is of this kind, because it has been proved in the Physics, Book VIII, that 
an unchangeable being exists. Now this unchangeable being is superior to and nobler than 


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changeable being, with which the philosophy of nature is concerned. And since the 
consideration of common being belongs to that science which studies the primary kind of 
being, then the consideration of common being belongs to a different science than the 
philosophy of nature. And the consideration of common principles of this kind will also 
belong to this science. For the philosophy of nature is a part of philosophy but not the first 
part, which considers common being and those attributes which belong to being as being. 

594. And whatever (324). 

Then he rejects the other false notion, which concerns the way in which such principles 
should be treated. For some men investigated these principles with the aim of demonstrating 
them. And whatever they said about the truth of these principles, i.e., how they must be 
accepted as true by force of demonstration, or how the truth found in all these principles must 
be reached, they did through ignorance of, or lack of skill in, "analytics," which is that part of 
logic in which the art of demonstration is treated. For "they must know these principles in 
order to attain scientific knowledge"; i.e., every science acquired by demonstration depends 
on these principles. 

But "those who are learning," i.e., the pupils who are being instructed in some science, must 
not seek these principles as something to be demonstrated. Or, according to another text, 
"those who have scientific knowledge must attain science from these principles"; i.e., those 
who attain knowledge by demonstration must come to know common principles of this kind 
and not ask that they be demonstrated to them. 

595. It is evident (325). 

He draws the conclusion primarily intended, namely, that it will be the function of the 
philosopher to consider every substance as such and also the first syllogistic principles. In 
order to make this clear it must be noted that self-evident propositions are those which are 
known as soon as their terms are known, as is stated in Book I of the Posterior Analytics. This 
occurs in the case of those propositions in which the predicate is given in the definition of the 
subject, or is the same as the subject. But it happens that one kind of proposition, even though 
it is self-evident in itself, is still not self-evident to all, i.e., to those who are ignorant of the 
definition of both the subject and the predicate. Hence Boethius says in De Hebdomadibus 
that there are some propositions which are self-evident to the learned but not to all. Now 
those are self-evident to all whose terms are comprehended by all. And common principles 
are of this kind, because our knowledge proceeds from common principles to proper ones, as 
is said in Book I of the Physics. Hence those propositions which are composed of such 
common terms as whole and part (for example, every whole is greater than one of its parts) 
and of such terms as equal and unequal (for example, things equal to one and the same thing 
are equal to each other), constitute the first principles of demonstration. And the same is true 
of similar terms. Now since common terms of this kind belong to the consideration of the 
philosopher, then it follows that these principles also fall within his scope. But the 
philosopher does not establish the truth of these principles (~) by way of demonstration, but 
(+) by considering the meaning of their terms. For example, he considers what a whole is and 
what a part is; and the same applies to the rest. And when the meaning of these terms 
becomes known, it follows that the truth of the above-mentioned principles becomes evident. 


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LESSON 6 

First Philosophy Must Examine the First Principle of Demonstration. The Nature of This 
Principle. The Errors about It 

ARISTOTLE'S TEXT Chapters 3 & 4: 1005b 8-1006a 18 

326. And it is fitting that the person who is best informed about each class of things should be 
able to state the firmest principles of his subject. Hence he who understands beings as beings 
should be able to state the firmest principles of all things. This person is the philosopher. 

327. And the firmest of all principles is that about which it is impossible to make a mistake; 
for such a principle must be both the best known (for all men make mistakes about things 
which they do not know) and not hypothetical. For the principle which everyone must have 
who understands anything about beings is not hypothetical; and that which everyone must 
know who knows anything must be had by him when he comes to his subject. It is evident, 
then, that such a principle is the firmest of all. 

328. And let us next state what this principle is. It is that the same attribute cannot both 
belong and not belong to the same subject at the same time and in the same respect; and let us 
stipulate any other qualifications that have to be laid down to meet dialectical difficulties. 
Now this is the firmest of all principles, since it answers to the definition given; for it is 
impossible for anyone to think that the same thing both is and is not, although some are of the 
opinion that Heraclitus speaks in this way; for what a man says he does not necessarily 
accept. But if it is impossible for contraries to belong simultaneously to the same subject (and 
let us then suppose that the same things are established here as in the usual proposition), and 
if one opinion which expresses the contradictory of another is contrary to it, evidently the 
same man at the same time cannot think that the same thing can both be and not be; for one 
who is mistaken on this point will have contrary opinions at the same time. And it is for this 
reason that all who make demonstrations reduce their argument to this ultimate position. For 
this is by nature the starting point of all the other axioms. 

Chapter 4 

329. Now as we have said (328), there are some who claimed that the same thing can both be 
and not be, and that this can be believed. And many of those who treat of nature adopt this 
theory. But now we take it to be impossible for a thing both to be and not be at the same time, 
and by means of this we shall show that this is the firmest of all principles. 

330. But some deem it fitting that even this principle should be demonstrated, and they do this 
through want of education. For not to know of what things one should seek demonstration and 
of what things one should not shows want of education. For it is altogether impossible that 
there should be demonstration of all things, because there would then be an infinite regress so 
that there would still be no demonstration. But if there are some things of which it is not 
necessary to seek demonstration, these people cannot say what principle they think to be more 
indemonstrable. 

331. But even in this case it is possible to show by refutation that this view is impossible, if 
only our opponent will say something. But if he says nothing, it is ridiculous to look for a 
reason against one who has no reason, on the very point on which he is without reason; for 
such a man is really like a plant. Now I say that demonstration by refutation is different from 


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demonstration [in the strict sense] , because he who would demonstrate this principle in the 
strict sense would seem to beg the question. But when someone argues for the sake of 
convincing another there will be refutation, not demonstration. 

COMMENTARY 

This science considers particularly the very first principle, that of contradiction. 

596. He shows here that it is the first philosopher who is chiefly concerned with the first 
principle of demonstration; and in regard to this he does two things. First, he shows that it is 
the business of the first philosopher to consider this principle; and second (611), he begins to 
examine this principle. 

In regard to the first he does three things.. First, he shows that it is the office of this science to 
consider the first principle of demonstration. Second (597), he indicates what this principle is. 
Third (606), he rejects certain errors regarding this same principle. 

In regard to the first point he uses the following argument. In every class of things that man is 
best informed who knows the most certain principles, because the certitude of knowing 
depends on the certitude of principles. But the first philosopher is best informed and most 
certain in his knowledge; for this was one of the conditions of wisdom, as was made clear in 
the prologue of this work (35), namely, that he who knows the causes of things has the most 
certain knowledge. Hence the philosopher ought to consider the most certain and firmest 
principles of beings, which he considers as the subject-genus proper to himself. 

597. And the firmest (327). 

Then he shows what the firmest or most certain principle is; and in regard to this he does two 
things. First, he states the conditions for the most certain principle; and then (600) he shows 
how they fit a single principle ("And let us"). 

He accordingly gives, first, the three conditions for the firmest principle. (1) The first is that 
no one can make a mistake or be in error regarding it. And this is evident because, since men 
make mistakes only about those things which they do not know, then that principle about 
which no one can be mistaken must be the one which is best known. 

598. (2) The second condition is that it must "not be hypothetical," i.e., it must not be held as 
a supposition, as those things which are maintained through some kind of common 
agreement. Hence another translation reads "And they should not hold a subordinate place," 
i.e., those principles which are most certain should not be made dependent on anything else. 
And this is true, because whatever is necessary for understanding anything at all about being 
"is not hypothetical," i.e., it is not a supposition but must be self-evident. And this is true 
because whatever is necessary for understanding anything at all must be known by anyone 
who knows other things. 

599. (3) The third condition is that it is not acquired (~) by demonstration or by any similar 
method, but (+) it comes in a sense by nature to the one having it inasmuch as it is naturally 
known and not acquired. For first principles become known through the natural light of the 
agent intellect, and they are not acquired by any process of reasoning but by having their 
terms become known. This comes about by reason of the fact that memory is derived from 
sensible things, experience from memory, and knowledge of those terms from experience. 


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And when they are known, common propositions of this kind, which are the principles of the 
arts and sciences, become known. 

Hence it is evident that the most certain or firmest principle should be such that there can be 
no error regarding it; that it is not hypothetical; and that it comes naturally to the one having 
it. 

600. And let us next (328). 

Then he indicates the principle to which the above definition applies. He says that it applies to 
this principle, as the one which is firmest: it is impossible for the same attribute both to 
belong and not belong to the same subject at the same time. And it is necessary to add "in the 
same respect"; and any other qualifications that have to be given regarding this principle "to 
meet dialectical difficulties" must be laid down, since without these qualifications there 
would seem to be a contradiction when there is none. 

601. That this principle must meet the conditions given above he shows as follows: (1) It is 
impossible for anyone to think, or hold as an opinion, that the same thing both is and is not at 
the same time, although some believe that Heraclitus was of this opinion. But while it is true 
that Heraclitus spoke in this way, he could not think that this is true; for it is not necessary 
that everything that a person says he should mentally an opinion. 

602. But if one were to say that it is possible for someone to think that the same thing both is 
and is not at the same time, this absurd consequence follows: contraries could belong to the 
same subject at the same time. And "let us suppose that the same things are established," or 
shown, here as in the usual proposition established in our logical treatises. For it was shown at 
the end of the Peri hermineas I that contrary opinions are not those which have to do with 
contraries but those which have to do with contradictories, properly speaking. For when one 
person thinks that Socrates is white and another thinks that he is black, these are not contrary 
opinions in the primary and proper sense; but contrary opinions are had when one person 
thinks that Socrates is white and another thinks that he is not white. 

603. Therefore, if someone were to think that two contradictories are true at the same time by 
thinking that the same thing both is and is not at the same time, he will have contrary opinions 
at the same time; and thus contraries will belong to the same thing at the same time. But this 
is impossible. It is impossible, then, for anyone to be mistaken in his own mind about these 
things and to think that the same thing both is and is not at the same time. And it is for this 
reason that all demonstrations reduce their propositions to this proposition as the ultimate 
opinion common to all; for this proposition is by nature the starting point and axiom of all 
axioms. 

604. (2 & 3) The other two conditions are therefore evident, because, insofar as those making 
demonstrations reduce all their arguments to this principle as the ultimate one by referring 
them to it, evidently this principle is not based on an assumption. Indeed, insofar as it is by 
nature a starting point, it clearly comes unsought to the one having it and is not acquired by 
his own efforts. 

605. Now for the purpose of making this evident it must be noted that, since the intellect has 
two operations, one by which it knows quiddities, which is called the understanding of 
indivisibles, and another by which it combines and separates, there is something first in both 
operations. In the first operation the first thing that the intellect conceives is being, and in this 


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operation nothing else can be conceived unless being is understood. 

And because this principle — it is impossible for a thing both to be and not be at the same 
time — depends on the understanding of being (just as the principle, every whole is greater 
than one of its parts, depends on the understanding of whole and part), then this principle is 
by nature also the first in the second operation of the intellect, i.e., in the act of combining and 
separating. And no one can understand anything by this intellectual operation unless this 
principle is understood. For just as a whole and its parts are understood only by understanding 
being, in a similar way the principle that every whole is greater than one of its parts is 
understood only if the firmest principle is understood. 

606. Now as we have said (329). 

Then he shows how some men erred regarding this principle; and in regard to this he does 
two things. First, he touches on the error of those who rejected the foregoing principle; and 
second (607) he deals with those who wished to demonstrate it ("But some"). 

He accordingly says that some men as was stated above about Heraclitus (601), said that the 
same thing can both be and not be at the same time, and that it is possible to hold this opinion; 
and many of the philosophers of nature adopt this position, as will be made clear below (665). 
For our part, however, we now take as evident that the principle in question is true, i.e., the 
principle that the same thing cannot both be and not be; but from its truth we show that it is 
most certain. For from the fact that a thing cannot both be and not be it follows that contraries 
cannot belong to the same subject, as will be said below (663). And from the fact that 
contraries cannot belong to a subject at the same time it follows that a man cannot have 
contrary opinions and, consequently, that he cannot think that contradictories are true, as has 
been shown (603). 

607. But some (330). 

Then he mentions the error of certain men who wished to demonstrate the above-mentioned 
principle; and in regard to this he does two things. First, he shows that it cannot be 
demonstrated in the strict sense; and second (608), that it can be demonstrated in a way ("But 
even"). 

Thus he says, first , that certain men deem it fitting, i.e., they wish, to demonstrate this 
principle; and they do this "through want of education," i.e., through lack of learning or 
instruction. For there is want of education when a man does not know what to seek 
demonstration for and what not to; for not all things can be demonstrated. For if all things 
were demonstrable, then, since a thing is not demonstrated through itself but through 
something else, demonstrations would either be circular (although this cannot be true, because 
then the same thing would be both better known and less well known, as is clear in Book I of 
the Posterior Analytics, or they would have to proceed to infinity. But if there were an infinite 
regress in demonstrations, demonstration would be impossible, because the conclusion of any 
demonstration is made certain by reducing it to the first principle of demonstration. But this 
would not be the case if demonstration proceeded to infinity in an upward direction. It is 
clear, then, that not all things are demonstrable. And if some things are not demonstrable, 
these men cannot say that any principle is more indemonstrable than the above-mentioned 
one. 

608. But even in this case (331). 


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Here he shows that the above-mentioned principle can be demonstrated in a certain respect. 
He says that it may be demonstrated by disproof. In Greek the word is evlegktikw/j, which is 
better translated as by refutation, for an e;legkoj is a syllogism that establishes the 
contradictory of a proposition, and so is introduced to refute some false position. And on 
these grounds it can be shown that it is impossible for the same thing both to be and not be. 

But this kind of argument can be employed only if the one who denies that principle because 
of difficulties "says something," i.e., if he signifies something by a word. But if he says 
nothing, it is ridiculous to look for a reason against one who does not make use of reason in 
speaking; for in this dispute anyone who signifies nothing will be like a plant, for even brute 
animals signify something by such signs. 

609. For it is one thing to give a strict demonstration of this principle, and another to 
demonstrate it argumentatively or by refutation. For if anyone wished to give a strict 
demonstration of this principle, he would seem to be begging the question, because any 
principle that he could take for the purpose of demonstrating this one would be one of those 
that depend on the truth of this principle, as is clear from what has been said above (330:C 
607). But when the demonstration is not of this kind, i.e., demonstration in the strict sense, 
there will then be disproof or refutation at most. 

610. Another text states this better by saying, "But when one argues for the sake of 
convincing another, there will then be refutation but not demonstration"; i.e., when a process 
of this kind from a less well known to a better known principle is employed for the sake of 
convincing another man who denies this, there will then be disproof or refutation but not 
demonstration; i.e., it will be possible to have a syllogism which contradicts his view, since 
what is less known absolutely is admitted by the opponent, and thus it will be possible to 
proceed to demonstrate the above-mentioned principle so far as the man is concerned but not 
in the strict sense. 


LESSON 7 

Contradictories Cannot Be True at the Same Time 
ARISTOTLE'S TEXT Chapter 4: 1006a 18-1007b 18 

332. The starting point of all such discussions is not the desire that someone shall state that 
something either is or is not, for this might perhaps be thought to be begging the question, but 
that he shall state something significant both for himself and for someone else; for this he 
must do if he is to say anything. For if he does not, no discussion will be possible for such a 
person either with himself or with another. But if anyone will grant this, demonstration will 
be possible; for there will already be something definite. But this will not have the effect of 
demonstrating but of upholding, for he who destroys reason upholds reason. 

333. First of all, then, it is evident that this at least is true, that the term to be or not to be 
signifies something, so that not everything will be so and not so. 

334. Again, if the term man signifies one thing, let this be a twofooted animal. 


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335. Now by signifying one thing I mean this: granted that man is a twofooted animal, then if 
something is a man, this will be what being a man is. And it makes no difference even if 
someone were to say that this term signifies many things, provided that there are a definite 
number; for a different term might be assigned to each concept. I mean, for example, that if 
one were to say that the term man signifies not one thing but many, one of which would have 
a single concept, namely, two-footed animal, there might still be many others, if only there 
are a limited number; for a particular term might be assigned to each concept. However, if 
this were not the case, but one were to say that a term signifies an infinite number of things, 
evidently reasoning would be impossible; for not to signify one thing is to signify nothing. 
And if words signify nothing, there will be no discourse with another or even with ourselves. 
For it is impossible to understand anything unless one understands one thing; but if this does 
happen, a term may be assigned to this thing. Let it be assumed, then, as we said at the 
beginning (332), that a term signifies something, and that it signifies one thing. 

336. It is impossible, then, that being a man should mean not being a man, if the term man 
not only signifies something about one subject but also signifies one thing. For we do not 
think it fitting to identify signifying one thing with signifying something about one subject, 
since the terms musical, white and man would then signify one thing. And therefore all things 
would be one, because all would be synonymous. And it will be impossible to be and not to 
be the same thing, except in an equivocal sense, as occurs if one whom we call man others 
call not-man. But the problem is not whether the same thing can at the same time be and not 
be a man in name, but whether it can in fact. 

337. Now if man and not-man do not signify something different, it is evident that not being a 
man will not differ from being a man. Thus being a man will be identical with not being a 
man, for they will be one thing. For being one means this: being related as clothing and 
garment are, if they are taken in the same sense. And if being a man and not being a man are 
to be one, they must signify one thing. But it has been shown that they signify different 
things. 

338. Therefore, if it is true to say that something is a man, it must be a two-footed animal, for 
this is what the term man signifies. But if this is necessary, it is impossible for this very thing 
not to be a two-footed animal; for this is what to-be-necessary means, namely, unable not to 
be. Hence it cannot be true to say that the same thing is and is not a man at the same time. The 
same argument also applies to not being a man. 

339. For being a man and not being a man signify different things, since being white and 
being a man are different; for there is much greater opposition in the former case, so that they 
signify different things. And if one were to say also that white signifies the same thing as man 
and is one in concept, we shall say the same thing as was said before (335), namely, that all 
things are one, and not merely opposites. But if this is impossible, then what has been said 
will follow. 

340. That is to say, it will follow if our opponent answers the question. And if in giving a 
simple answer to the question he also adds the negations, he is not answering the question. 
For there is nothing to prevent the same thing from being man and white and a thousand other 
things numerically. Still if one asks whether it is or is not true to say that this is a man, his 
opponent should reply by stating something that means one thing and not add that it is also 
white or black or large. Indeed, it is impossible to enumerate the accidents of being, which are 
infinite in number; so therefore let him enumerate either all or none. Similarly, even if the 
same thing is a thousand times a man and a not-man, he must not, in answering the question 


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whether this is a man, add that it is also at the same time a not-man, unless he also gives all 
the other corresponding accidents, whatever are so or are not so. And if he does not do this, 
there will be no debate with him. 

341. And those who say this do away completely with substance or essence, for they must say 
that all attributes are accidents, and that there is no such thing as being a man or being an 
animal. For if there is to be such a thing as being a man, this will not be being a not-man or 
not being a man; in fact these are the negations of it. For there was one thing which the term 
signified, and this was the substance of something. And to signify the substance of a thing is 
to signify that its being is not something else. And if being essentially a man is being 
essentially a not-man, then the being of man will be something else. Hence they are 
compelled to say that nothing will have such a concept as this, but that all attributes are 
accidental. For this distinguishes substance from accident; for white is an accident of man, 
because while some man is white he is not the essence of whiteness. 

342. Moreover, if all attributes are accidental predicates, there will be no first universal. And 
if the accidental always implies a predication about some subject, the process must go on to 
infinity. But this is impossible; for not more than two terms are combined in accidental 
predication. For an accident is an accident of an accident only because both are accidents of 
the same subject. I mean, for example, that white is an accident of musical and musical of 
white' only because both are accidental to man; but Socrates is not musical in the sense that 
both are accidental to something else. Therefore, since some accidents are predicated in the 
latter and some in the former sense, all those that are predicated as white is predicated of 
Socrates cannot form an infinite series in an upward direction so that there should be another 
accident of white Socrates; for no one thing results from all of these. Nor again will white 
have another accident, such as musical; for this is no more an accident of that than that of this. 
And at the same time it has been established that some things are accidents in this sense and 
some in the sense that musical is an accident of Socrates. And whatever attributes are 
predicated accidentally in the latter sense are not accidents of accidents but only those 
predicated in the former sense. Not all attributes, then, are said to be accidents; and thus there 
must be some term which also signifies substance. And if this is so, then we have proved that 
contradictories cannot be predicated at the same time of the same subject. 

COMMENTARY 

611. Here he begins to argue dialectically against those who deny the foregoing principle, and 
this is divided into two parts. In the first (332:C 61 1) he argues against those who say that 
contradictories are true at the same time; and in the second (383:C 720), against those who 
say that they are false at the same time ("Neither can there be"). 

In regard to the first he does two things. First, he argues in a general way against those who 
make the aforesaid errors. Second (353 :C 663), he shows how we must argue specifically 
against different positions ("But the same method"). 

In regard to the first he does two things. First, he argues dialectically against the reasoning of 
those who deny the foregoing principle. Second (352:C 661), he shows that Protagoras' 
opinion is fundamentally the same as the one just mentioned ("The doctrine of Protagoras"). 

In regard to the first point he gives seven arguments. He gives the second (341 :C 624) at the 
words "And those who"; the third (343:C 636) at "Furthermore, if all"; the fourth (347:C 642) 
at "Again, either this"; the fifth (348:C 652) at "Again, how"; the sixth (349:C 654) at "It is 


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most evident"; and the seventh (351:C 65.9) at "Further, even if all." 

In regard to the first he does two things. First, he indicates the starting point from which one 
must proceed to argue against those who deny the first principle. Second (333:C 612), he 
proceeds to argue from that starting point ("First of all, then"). 

He therefore says, first (332), that with respect to all such unreasonable positions there is no 
need for us to take as a starting point that someone "wishes to suppose that this thing 
definitely is "or is not"; i.e., it is not necessary to take as a starting point some proposition in 
which some attribute is either affirmed or denied of a subject (for this would be a begging of 
the question, as was said above [331:C 609] ), but it is necessary to take as a starting point 
that a term signifies something both to the one who utters it, inasmuch as he himself 
understands what he is saying, and to someone else who hears him. But if such a person does 
not admit this, he will not say anything meaningful either for himself or for someone else, and 
it will then be idle to dispute with him. But when he has admitted this, a demonstration 

will at once be possible against him; for there is straightway found to be something definite 
and determinate which is signified by the term distinct from its contradictory, as will become 
clear below. Yet this will not strictly be a demonstration of the foregoing principle but only 
an argument upholding this principle against those who deny it. For he who "destroys 
reason," i.e., his own intelligible expression, by saying that a term signifies nothing, must 
uphold its significance, because he can only express what he denies by speaking and by 
signifying something. 

612. First of all, then (333). 

He proceeds from the assumption he had made to prove what he intends. First, he deals with 
one particular case; and second (334:C 612), he treats all cases in a general way ("Again, if 
the term"). 

He accordingly says, first (333), that if a term signifies something, it will be evident first of 
all that this proposition will be true, and that its contradictory, which he denies, will be false; 
and thus this at least will be true, that not every affirmation is true together with its negation. 

613. Now by signifying (535). 

Then he shows that this applies universally to all cases, namely, that contradictories are not 
true at the same time. In regard to this he does four things. First, he makes certain 
assumptions which are necessary for drawing his intended conclusion. Second (338:C 620), 
he draws his conclusion ("Therefore, if it is true"). Third (339:C 622), he proves one 
assumption which he had made ("For being a man"). Fourth (340:C 623), he rejects a quibble 
("That is to say"). 

In regard to the first he does three things. First, he shows that a term signifies one thing; and 
second (336:C 616), he shows from this that the term man signifies what being a man is, but 
not what it is not ("It is impossible, then"). Third (337:C 61g), he shows that the term man 
signifies one thing ("Now if man"). 

He accordingly says, first (335), that if the term man signifies one thing, let this be two-footed 
animal. For a term is said to signify this one thing which is the definition of the thing 
signified by the term, so that if "twofooted animal" is the being of man, i.e., if this is what the 


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essence of man is, this will be what is signified by the term man. 

614. But if one were to say that a term signifies many things, it will signify either a finite or 
an infinite nurnher of them. But if it signifies a finite number, it will differ in no way, 
according to another translation, from the term which is assumed to signify one thing; for it 
signifies many finite concepts of different things, and different terms can be fitted to each 
single concept. For example, if the term man were to signify many concepts, and the concept 
two-footed animal is one of them, one term is assigned to the concept man. And if there are 
many other concepts, many other terms may be assigned so long as those concepts are finite 
in number. Thus he will be forced back to the first position, that a term signifies one thing. 

615. But if a term does not signify a finite but an infinite number of concepts, evidently 
neither reasoning nor debate will be possible. This becomes clear as follows: any term that 
does not signify one thing signifies nothing. This is proved thus: terms signify something 
understood, and therefore if nothing is understood, nothing is signified. But if one thing is not 
understood, nothing is understood, because anyone who understands anything must 
distinguish it from other things. If a term does not signify one thing, then, it signifies nothing 
at all; and if terms signify nothing, discourse will be impossible, both the kind which 
establishes truth and the kind which refutes an assertion. Hence it is clear that, if terms signify 
an infinite number of things, neither reasoning nor dispute will be possible. But if it is 
possible to understand one thing, a term may be given to it. So let it be held then that a term 
signifies something. 

616. It is impossible (336). 

He proves the second point, namely, that the term man does not signify not being a man; for a 
term that signifies one thing signifies not only what is one in subject (and is therefore said to 
be one because it is predicated of one subject) but what is one absolutely, i.e., in concept. For 
if we wanted to say that a term signifies one thing because it signifies the attributes which are 
verified of one thing, it would then follow that the terms musical, white and man all signify 
one thing, since all are verified of one thing. And from this it would follow that all things are 
one; for if white is predicated of man and is therefore identical with him, then when it is also 
predicated of a stone it will be identical with a stone; and since those things which are 
identical with one and the same thing are identical with each other, it would follow that a man 
and a stone are one thing and have one concept. Thus the result would be that all terms are 
univocal, i.e., one in concept, or synonymous, as another text says, i.e., meaning absolutely 
the same thing in subject and in concept. 

617. Now although being and nonbeing are verified of the same subject according to those 
who deny the first principle, still being a man and not being a man must differ in concept, just 
as white and musical differ in concept even though they are verified of the same subject. 
Hence it is evident that being and non-being cannot be the same in concept and in subject in 
the sense that they are signified by one univocal term. 

618. Now it must be noted that the expression being a man or to be a man or having the being 
of a man is taken here for the quiddity of man, and therefore it is concluded from this that the 
term man does not signify not being a man as its proper concept. But because he had said 
above (335:C 614) that the same term can signify many things according to different 
concepts, he therefore adds "except in an equivocal sense" in order to make clear that the 
term man does not signify in a univocal sense both being a man and not being a man, but it 
can signify both in an equivocal sense; i.e., in the sense that what we call man in one 


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language others might call not-man in another language. For we are not debating whether the 
same thing can both be and not be man in name, but whether it can in fact. 

619. Now if man (337). 

Then he proves the third point: that the terms man and not-man do not signify the same thing, 
and he uses the following argument. The term man signifies being a man or what man is, and 
the term not-man signifies not being a man or what man is not. If, then, man and not man do 
not signify something different, being a man will not differ from not being a man, or being a 
n6t-man, and therefore one of these will be predicated of the other. And they will also have 
one concept; for when we say that some terms signify one thing, we mean that they signify 
one concept, as the terms clothing and garment do. Hence, if being a man and not being a 
man are one in this way, i.e., in concept, there will then be one concept which will signify 
both being a man and not being a man. But it has been granted or demonstrated that the term 
which signifies each is different; for it has been shown that the term man signifies man and 
does not signify not-man. Thus it is clear that being a man and not being a man do not have a 
single concept, and therefore the thesis that man and not-man signify different things becomes 
evident. 

620. Therefore, if it is true (338). 

Here he proves his main thesis from the assumptions made earlier, and he uses the following 
argument. A man must be a two-footed animal, as is true from the foregoing, for this is the 
concept which the term man signifies. But what is necessary cannot not be; for this is what 
the term necessary means, namely, unable not to be, or incapable of not being, or impossible 
not to be. Hence it is not possible, or incapable, or impossible for man not to be a two-footed 
animal, and therefore it is evident that the affirmation and the negation cannot both be true; 
i.e., it cannot be true that man is both a two-footed animal and not a two-footed animal. The 
same reasoning based on the meanings of terms can be understood to apply to what is 
not-man, because what is not-man must be not a two-footed animal, since this is what the 
term signifies. Therefore it is impossible that a not-man should be a two-footed animal. 

621. Now the things demonstrated above are useful to his thesis, because if someone were to 
think that the terms man and not-man might signify the same thing, or that the term man 
might signify both being a man and not being a man, his opponent could deny the proposition 
that man must be a two-footed animal. For he could say that it is no more necessary to say 
that man must be a two-footed animal than to say that he is not a two-footed animal, granted 
that the terms man and not-man signify the same thing, or granted that the term man signifies 
both of these-being a man and not being a man. 

622. For being a man (339) 

Then he proves one of the assumptions which he had made; for in order to prove that the term 
man does not signify not being a man, he assumed that being a man and not being a man are 
different, even though they might be verified of the same subject. His aim here is to prove this 
by the following argument. There is greater opposition between being a man and not being a 
man than between man and white; but man and white have different concepts, although they 
may be the same in subject. Therefore being a man and not being a man also have different 
concepts. He proves the minor thus: if all attributes which are predicated of the same subject 
have the same concept and are signified by one term, it follows that all are one, as has been 
stated and explained (336:C 616). Now if this is impossible, the position we have maintained 


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follows, namely, that being a man and not being a man are different. And for this reason the 
final conclusion given above will follow, namely, that man is a two-footed animal, and that it 
is impossible for him to be what is not a two-footed animal. 

623. That is to say (340). 

He rejects one quibble by which the foregoing process of reasoning could be obstructed. For 
when an opponent has been asked whether man must be a two-footed animal, he need not 
reply either affirmatively or negatively but could say that man must be both a two-footed 
animal and not a two-footed animal. But the philosopher rejects this here, saying that the 
foregoing conclusion follows so long as an opponent wishes to give a simple answer to the 
question. But if in giving a simple answer to the question on the side of the affirmative he 
also wishes to include in his answer the negative aspect, he will not be answering the 
question. He proves this as follows. One and the same thing can be both a man and white and 
a thousand other things of this kind. Yet if it is asked here whether a man is white, we must 
give in our answer only what is signified by one word, and not add all the other attributes. For 
example, if one asks whether this is a man, we must answer that it is a man, and not add that it 
is both a man and white and large and the like; for we must give either all of the accidents of 
a thing at once or not. But not all accidents can be given at once since they are infinite in 
number; for there are an infinite number of accidents belonging to one and the same thing by 
reason of its relationship to an infinite number of antecedents and consequents, and what is 
infinite in number cannot be traversed. In answering the question, then, we must not give any 
of the attributes which are accidental to the thing about which the question is raised but only 
the attribute which is asked for. Hence, even if it is supposed a thousand times that man and 
not-man are the same, still, when the question is asked about man, the answer must not 
include anything about not-man, unless all those things which are accidental to man are given. 
And if this were done, no dispute would be possible, because it would never reach 
completion, since an infinite number of things cannot be traversed. 

624. And those who (341). 

Then he gives the second argument, and it is based on the notion of substantial and accidental 
predicates. This is his argument: if an affirmation and a negation are verified of the same 
subject, it follows that no term will be predicated quidditatively, or substantially, but only 
accidentally; and therefore there will have to be an infinite regress in accidental predicates. 
But the consequent is impossible, and thus the antecedent must be impossible. 

625. In this argument he does two things. First, he gives a conditional proposition. Second 
(342:C 629), he gives a proof that destroys the consequent ("Moreover, if all"). 

Regarding the first part he proceeds as follows. He says that those who state that an 
affirmation ind a negation may lie true at the same time completely do away with 
"substance," i.e., with a 

substantial predicate, "or essence," i.e., with an essential predicate; for they must say "that all 
attributes are accidents," or accidental predicates, and that there is no such thing as being a 
man or being an animal, and that what the quiddity of man or the quiddity of animal signifies 
does not exist. 

626. He proves this as follows: if there is something which is being a man, i.e., which is the 
substantial essence of man, which is predicated of man, it will not be not being a man or 


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being a not-man; for these two, i.e., not being a man and being a not-man, are the negations of 
being a man. It is clear, then, that an affirmation and a negation are not verified of the same 
subject, for not being a man or being a not-man is not verified of being a man. 

627. And the assumption made, namely, that if there is such a thing as being a man, this will 
not be not being a man or being a not-man, he proves in the following way. It was posited and 
proved above that the thing which a term signifies is one. And it was also posited that the 
thing which a term signifies is the substance of something, namely, a thing's quiddity. Hence 
it is clear that some term signifies a thing's substance, and that the thing which was signified 
is not something else. Therefore, if the essence or quiddity of man should be either not being 
a man or being a not-man, it is quite clear that it would differ from itself. It would be 
necessary to say, then, that there is no definition signifying a thing's essence. But from this it 
would follow that all predicates are accidental ones. 

628. For substance is distinguished from accident, i.e., a substantial predicate is distinguished 
from an accidental one, in that each thing is truly what is predicated substantially of it. Thus it 
cannot be said that a substantial predicate is not one thing, for each thing exists only if It is 
one. But man is said to be white because whiteness or white is one of his accidents, although 
not in such a way that he is the very essence of white or whiteness. It is not necessary, then, 
that an accidental predicate should be one only, but there can be many accidental predicates. 
A substantial predicate, however, is one only; and thus it is clear that what being a man is is 
not what not being a man is. But if a substantial predicate is both, it will no longer be one 
only, and thus will not be substantial but accidental. 

629. Moreover, if all (342). 

He destroys the consequent. He shows that it is impossible that all predicates should be 
accidental and none substantial because, if all were accidental, there would be no universal 
predicate. (And universal predicate here means the same thing as it does in the Posterior 
Analytics, i.e., an attribute which is predicated of something in virtue of itself and in reference 
to what it itself is). But this is impossible; for if one attribute is always predicated of another 
accidentally, there will be an infinite regress in accidental predication; but this is impossible 
for this reason. 

630. For there are only two ways in which accidental predication occurs. One way is had 
when one accident is predicated accidentally of another; and this happens because both are 
accidents of the same subject, for example, when white is predicated of musical because both 
are accidents of man. The other way is had when an accident is predicated of a subject (as 
when Socrates is said to be musical), not because both are accidents of some other subject, 
but because one of them is an accident of the other. Hence, even though there are two ways in 
which accidents may be predicated, in neither way can there be an infinite regress in 
predication. 

63 1 . For it is clear that there cannot be an infinite regress in that way in which one accident is 
predicated of another, because one must reach some subject. For it has been stated already 
that the essential note of this kind of predication is that both accidents are predicated of one 
subject. And thus by descending from a predicate to a subject, the subject itself can be found 
to be the terminus. 

632. And there cannot be an infinite regress in an upward direction in the way of predicating 
in which an accident is predicated of a subject, as when Socrates is said to be white, by 


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ascending from a subject to a predicate so as to say that white is an accident of Socrates and 
that some other attribute is an accident of white Socrates. For this could occur only in two 
ways. One way would be that one thing would come from white and Socrates; and thus just as 
Socrates is one subject of whiteness, in a similar way white Socrates would be one subject of 
another accident. But this cannot be so, because one thing does not come from all of these 
predicates. For what is one in an absolute sense does not come from a substance and an 
accident in the way that one thing comes from a genus and a difference. Hence it cannot be 
said that white Socrates is one subject. 

633. The other way would be that, just as Socrates is the subject of whiteness, in a similar 
way some other accident, such as musical, would have whiteness as its subject. But neither 
can this be so, and for two reasons. First, there can be no special reason why musical should 
be said to be an accident of white rather than the reverse; neither white nor musical will be 
prior to the other, but they will rather be of equal rank. Second, in conjunction with this it has 
been established or determined at the same time that this way of predicating in which an 
accident is predicated of an accident differs from that in which an accident is predicated of a 
subject, as when musical is predicated of Socrates. But in the way of which he is now 
speaking accidental predication does not mean that an accident is predicated of an accident; 
but it is to be so taken in the way we first described. 

634. It is evident, then, that an infinite regress in accidental predication is impossible, and 
therefore that not all predications are accidental. And it is also evident that there will be some 
term which signifies substance; and again, that contradictories are not true of the same 
subject. 

635. Now with regard to the argument given it must be noted that, even though one accident 
is not the subject of another, and thus one accident is not related to the other as its subject, 
still one is related to the other as cause and thing caused. For one accident is the cause of 
another. Heat and moistness, for example, are the cause of sweetness, and surface is the cause 
of color. For by reason of the fact that a subject is receptive of one accident it is receptive of 
another. 


LESSON 8 

Other Arguments Against the Foregoing Position 
ARISTOTLE'S TEXT Chapter 4: 1007b 18-1008b 2 

343. Furthermore, if all contradictories are true of the same subject at the same time, it is 
evident that all things will be one. For the same thing will be a trireme, a wall and a man, if it 
is possible either to affirm or to deny anything of everything. 

344. And this is what must follow for those who agree with Protagoras' view. For if it appears 
to anyone that a man is not a trireme, it is evident that he is not a trireme; so that he also is a 
trireme if contradictories are true. And thus there arises the view of Anaxagoras that all things 
exist together at the same time, so that nothing is truly one. Hence they seem to be speaking 
about the indeterminate; and while they think they are speaking about being, they are 
speaking about non43eing; for the indeterminate is what exists potentially and is not complete. 


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345. But the affirmation and the negation of every predicate of every subject must be 
admitted by them; for it would be absurd if each subject should have its own negation 
predicated of it while the negation of something else which cannot be predicated of it should 
not be predicated of it. I mean that, if it is true to say that a man is not a man, evidently it is 
also true to say that he is not a trireme. Therefore, if the affirmation is predicable of him, so 
also must the negation be. But if the affirmation is not predicable of him, the negation of the 
other term will be predicable of him to a greater degree than his own negation. If, then, the 
latter negation is predicable of him, the negation of trireme will also be predicable of him; 
and if this is predicable of him, the affirmation will be too. This is what follows, then, for 
those who hold this view. 

346. And it also follows for them that it is not necessary either to affirm or to deny. For if it is 
true that the same thing is both a man and a not-man, evidently it will be neither a man nor a 
not-man; for of the two affirmations there are two negations. And if the former is taken as a 
single proposition composed of the two, the latter also will be a single proposition opposed to 
the former. 

347. Again, either this is true of all things, and a thing is both white and not-white, and both 
being and not-being, and the same applies to other affirmations and negations; or it is not true 
of all but is true of some and not of others. And if not of all, the exceptions will be admitted. 
But if it is true of all, then either the negation will be true of everything of which the 
affirmation is, and the affirmation will be true of everything of which the negation is, or the 
negation will be true of everything of which the affirmation is, but the affirmation will not 
always be true of everything of which the negation is. And if the latter is true, there will be 
something that certainly is not, and this will be an unshakeable opinion. 

And if that it is not is something certain and knowable, more known indeed will be the 
opposite affirmation than the negation. But if in denying something it is equally possible to 
affirm what is denied, it is necessary to state what is true about these things, either separately 
(for example, to say that a thing is white and that it is not-white), or not. And if it is not true 
to affirm them separately, then an opponent will not be saying what he professes to say, and 
nothing will exist. But how could non-existent things speak or walk, as he does? Again, 
[according to this view] all things will be one, as has been said before (336:C 616), and man 
and God and a trireme and their contradictories will be the same. Similarly, if this is true of 
each thing, one thing will differ in no respect from another; for if it differs, this difference 
will be something true and proper to it. And similarly if it is possible for each to be true 
separately, the results described will follow. And to this we may add that all will speak the 
truth and all speak falsely; and that each man will admit of himself that he is in error. And at 
the same time it is evident that up to this point the discussion is about nothing at all, because 
our opponent says nothing. For he does not say that a thing is so or is not so, but that it is both 
so and not so; and again he denies both of these and says that it is neither so nor not so. For if 
this were not the case there would already be some definite statement. Further, if when the 
affirmation is true the negation is false, and if when the negation is true the affirmation is 
false, it will be impossible both to affirm and to deny the same thing truly at the same time. 
But perhaps someone will say that this was the contention from the very beginning. 

COMMENTARY 

636. Then he gives a third argument, which involves oneness and difference. The argument 
runs thus: if an affirmation and a negation are true of the same subject at the same time, all 
things will be one. But the consequent is false. Hence the antecedent must be false. In regard 


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to this argument he does three things. 

First (343 :C 636), he lays down a conditional proposition and gives an example, namely, that 
if contradictories are true of the same subject at the same time, it will follow that the same 
thing will be a trireme (i.e., a ship with three banks of oars), a wall and a man. 

637. And this is what (344). 

Then he shows that the same impossible conclusion follows with regard to two other 
positions. He does this, first, with regard to the opinion of Protagoras, who said that whatever 
seems so to anyone is wholly true for him; for if it seems to someone that a man is not a 
trireme, then he will not be a trireme; and if it seems to someone else that a man is a trireme, 
he will be a trireme; and thus contradictories will be true. 

638. Second, he does this with regard to the opinion of Anaxagoras, who said that all things 
exist together, so that nothing which is truly one is distinguished from other things, but all are 
one in a kind of mixture. For he said that everything is found in everything else, as has been 
shown in Book I of the Physics. This is the position which Anaxagoras adopted because he 
seems to be speaking about indeterminate being, i.e., what has not been made actually 
determinate. And while he thought he was speaking about complete being, he was speaking 
about potential being, as will become clear below (355:C 667). But the indeterminate is what 
exists potentially and is not "complete," i.e., actual; for potency is made determinate only by 
actuality. 

639. But the affirmation (345). 

Third, he proves that the first conditional proposition is true. He does this, first, on the 
grounds that all things would have to be affirmed to be one; and second (346:C 640), on the 
grounds that affirmations would not be distinguished from their negations from the viewpoint 
of truth and falsity ("And it also follows"). 

He accordingly says, first (345), that the first conditional proposition must be admitted by 
them inasmuch as they hold than an affirmation and a negation are true of the same subject at 
the same time because an affirmation and a negation are true of anything at all. For it is clear 
that the negation of some other thing seems to be predicable of each thing to a greater degree 
than its own negation. For it would be absurd if some subject should have its own negation 
predicated of it and not the negation of something else by which it is signified that this other 
thing is not predicable of it. For example, if it is true to say that a man is not a man, it is much 
truer to say that a man is not a trireme. Hence it is clear that anything of which a negation 
must be predicated must also have an affirmation predicated of it. Therefore a negation will 
be predicated of it since an affirmation and a negation are true at the same time; or if an 
affirmation is not predicated of it, the negation of the other term will be predicated of it to a 
greater degree than its own negation. For example, if the term trireme is not predicable of 
man, non-trireme will be predicated of him inasmuch as it may be said that a man is not a 
trireme. But if the affirmation is predicable, so also must the negation be, since they are 
verified of the same thing. A man, then, must be a trireme, and he must also be anything else 
on the same grounds. Hence all things must be one. Therefore this is what follows for those 
who maintain the position that contradictories are true of the same subject. 

640. And it also follows (346). 


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He now draws the other impossible conclusion which follows from this view, namely, that a 
negation will not be distinguished from an affirmation as regards falsity, but each will be 
false. Thus he says that not only the foregoing impossible conclusions follow from the 
above-mentioned position, but also the conclusion that it is not necessary "either to affirm or 
to deny," i.e., it is not necessary that either the affirmation or the negation of a thing should be 
true, but each may be false; and so there will be no difference between being true and being 
false. He' proves this as follows. 

641. If it is true that something is both a man and a not-man, it is also true that it is neither a 
man nor a not-man. This is evident. For of these two terms, man and not-man, there are two 
negations, not man and not not-man. And if one proposition were formed from the first two, 
for example, if one were to say that Socrates is neither a man nor a not-man, it would follow 
that neither the affirmation nor the negation is true but that both are false. 

642. Again, either this (347). 

Then he gives a fourth argument, and this is based on certitude in knowing. It runs thus. If an 
affirmation and a negation are true at the same time, either this is true of all things, or it is true 
of some and not of others. But if it is not true of all, then those of which it is true will be 
"admitted"; i.e., they will be conceded simply and absolutely, or according to another 
translation "they will be certain," i.e., true with certainty; that is, in their case the negation 
will be true because the affirmation is false, or the reverse. 

643. But if it is true in all cases that contradictories are verified of the same subject, this might 
happen in two ways. In one way anything of which affirmations are true, negations are true, 
and the reverse. In another way anything of which affirmations are true, negations are true, 
but not the reverse. 

644. And if the second is true, this impossible conclusion will follow: there will be something 
that firmly or certainly is not; and so there will be an unshakeable opinion regarding a 
negative proposition. And this will be the case because a negation is always true since 
whenever an affirmation is true its negation is also true. But an affirmation will not always be 
true, because it was posited that an affirmation is not true of anything at all of which a 
negation is true; and thus a negation will be more certain and knowable than an affirmation. 
But this seems to be false because, even though non-being is certain and knowable, an 
affirmation will always be more certain than its opposite negation; for the truth of a negation 
always depends on that of some affirmation. Hence a negative conclusion can be drawn only 
if there is some kind of affirmation in the premises. But an affirmative conclusion can never 
be drawn from negative premises. 

645. Now if one were to speak in the first way and say that of anything of which an 
affirmation is true the negation is also true, and similarly that of anything of which the 
negation is true the affirmation is also true, inasmuch as affirmation and negation are 
interchangeable, this might happen in two ways. For if an affirmation and a negation are both 
true at the same time, either it will be possible to state what is true of each separately, for 
example, to say that each of these propositions is true separately — "Man is white" and "Man 
is not white"; or it will not be possible to state that each is true separately but only both 
together. For example, if we were to say that this copulative proposition is true — "Man is 
white and man is not white." 


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646. And if we were to speak in the second way and say that neither one is true separately but 
only both together, two impossible conclusions would then follow. The first is that "an 
opponent will not be saying what he professes to say," i.e., he will assert neither the 
affirmation nor the negation of something, and "neither will exist," i.e., both will be false; or 
according to another text, "nothing will exist," i.e., it will follow that nothing is true, neither 
the affirmation nor the negation. And if nothing is true it will be impossible to understand or 
to express anything. For how can anyone understand or express non-being? Implied is the 
reply: in no way. 

647. The second impossible conclusion would be that all things are one, as has been stated in 
a previous argument (345 :C 639). For it would follow that a man and God and a trireme, and 
also their contradictories, a notman, not-God and not-trireme, are the same. Thus it is clear 
that, if an affirmation and a negation are true of any subject at the same time, one thing will 
not differ from another. For if one were to differ from another, something would have to be 
predicated of the one which is not predicated of the other; and so it would follow that 
something is definitely and properly true of this thing which does not fit the other. Therefore 
an affirmation and a negation will not be true of anything whatever. But it is clear that things 
which differ in no way are one. Thus it would follow that all things are one. 

648. But if one were to speak in the first way and say that it is possible for an affirmation and 
a negation to be true, not only together but also separately, four impossible conclusions will 
follow. The first is that this position "indicates that this statement is true"; i.e., it proves that 
the statement just made is true. Hence another text reads, "the results described will follow," 
i.e., all things will be one, because it will then be possible both to affirm and to deny each 
thing, and one will not differ from the other. 

649. A second impossible conclusion is that all will speak the truth, because anyone at all 
must make either an affirmation or a negation, and each will be true. And each man will also 
admit of himself that he is wrong when he says that the affirmation is true; for, since he says 
that the negation is true, he admits that he was in error when he made the affirmation. 

650. A third impossible conclusion is that up to this point there obviously could not be any 
investigation or dispute. For it is impossible to carry on a dispute with someone who admits 
nothing, because such a person really says nothing since he does not say absolutely that 
something is so or is not so; but he says that it is both so and not so. And again he denies both 
of these, for he says that it is neither so nor not so, as is evident from the preceding argument. 
For if he does not deny all of these he will know that something is definitely true, and this is 
contrary to his original position. Or according to another translation which expresses this 
more clearly, "there would already be some definite statement." 

65 1 . A fourth impossible conclusion will follow because of the definition of the true and the 
false. For truth exists when one says that what is, is, or that what is not, is not. But falsity 
exists when one says that what is, is not, or that what is not, is. Hence from the definition of 
the true and the false it is clear that, when an affirmation is true, its negation is false; for one 
then says that what is, is not. And when a negation is true, its affirmation is false; for what is 
not is then said to be. Therefore it is impossible both to affirm and to deny the same thing 
truly. But perhaps an opponent could say that this last argument is begging the questiofi; for 
he who claims that contradictories are true at the same time does not accept this definition of 
the false: the false is to say that what is not, is, or that what is, is not. 


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LESSON 9 

Three Further Arguments Against Those Who Deny the First Principle 
ARISTOTLE'S TEXT Chapters 4 & 5: 1008b 2-1009a 16 

348. Again, how is that man wrong who judges that a thing is so or is not so, and is he right 
who judges both? For if the second is right, what will his statement mean except that such is 
the nature of beings? And if he is not right, he is more right than the one who holds the first 
view, and beings will already be of a certain nature, and this will be true and not at the same 
time not true. But if all men are equally right and wrong, anyone who holds this view can 
neither mean nor state anything; for he will both affirm and not affirm these things at the 
same time. And if he makes no judgment but equally thinks and does not think, in what 
respect will he differ from plants? 

349. It is most evident, then, that no one, either among those who profess this theory or any 
others, is really of this mind. For why does a man walk home 1 and not remain where he is 
when he thinks he is going there? He does not at dawn walk directly into a well or into a 
brook if he happens on such; but he seems to be afraid of doing so because he does not think 
that to fall in is equally good and not good. Therefore he judges that the one is better and the 
other not. And if this is so in the case of what is good and what is not good, it must also be so 
in the case of other things. Thus he must judge that one thing is a man and another not a man, 
and that one thing is sweet and another not sweet. For when he thinks that it is better to drink 
water and to see a man and then seeks these things, he does not make the same judgment 
about all of them, though this would be necessary if the same thing were equally a man and 
not a man. But according to what has been said there is no one who does not seem to fear 
some things and not others. Hence, as it appears, all men make an unqualified judgment, and 
if not about all things, still about what is better or worse. 

350. And if they do not have science but opinion, they ought to care all the more about the 
truth, just as one who is ill ought to care more about health than one who is well. For one who 
has opinion in contrast to one who has science is not healthily disposed towards the truth. 

35 1 . Further, even if all things are so and not so as much as you like, still difference of degree 
belongs to the nature of beings. For we should not say that two and three are equally even; 
and he who thinks that four is five is not equally as wrong as he who thinks that it is a 
thousand. Therefore, if they are not equally wrong, obviously one is less wrong and so more 
right. Hence, if what is truer is nearer to what is true, there must be some truth to which the 
truer is nearer. And even if there is not, still there is already something truer and more certain, 
and we shall be freed from that intemperate theory which prevents us from determining 
anything in our mind. 

Chapter 5 

352. The doctrine of Protagoras proceeds from the same opinion, and both of these views 
must be alike either true or not true. For if all things which seem or appear are true, 
everything must be at once true and false. For many men have opinions which are contrary to 
one another, and they think that those who do not have the same opinions as themselves are 


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wrong. Consequently the same thing must both be and not be. And if this is so, it is necessary 
to think that all opinions are true; for those who are wrong and those who are right entertain 
opposite opinions. If, then beings are such, all men will speak the truth. Hence it is evident 
that both contraries proceed from the same way of thinking. 

COMMENTARY 

652. Here he gives a fifth argument, which is based on the notion of truth, and it runs as 
follows. It has been stated that both the affirmation and the negation of something are held to 
be true at the same time. Therefore he who judges or thinks that "a thing is so," i.e., that the 
affirmation alone is true, "or is not so," i.e., that the negation alone is true, is wrong; and he 
who judges that both are true at the same time is right. Hence, since truth exists when 
something is such in reality as it is in thought, or as it is expressed in words, it follows that 
what a man expresses will be something definite in reality; i.e., the nature of beings will be 
such as it is described to be; so that it will not be at once the subject both of an affirmation 
and of a negation. Or according to another text, "beings will already be of a certain nature," as 
if to say that since the statement is definitely true, it follows that a thing has such a nature. 
However, if one were to say that it is not he who judges that an affirmation and a negation are 
true at the same time that has a true opinion, but rather he who thinks that either the 
affirmation alone is true or the negation alone is true, it is evident that beings will already 
exist in some determinate way. Hence another translation says more clearly, "and in a sense 
this will be definitely true and not at the same time not true," because either the affirmation 
alone is true or the negation alone is true. 

653. But if all of those just mentioned, i.e., both those who affirm both parts of a 
contradiction and those who affirm one of the two, "are wrong," and all are also right, it will 
be impossible to carry on a dispute with anyone who maintains this, or even to say anything 
that might provoke a dispute with him. Or according to another text, "such a man will not 
affirm or assert anything." For, as another translation says, "he cannot assert or affirm 
anything of this kind," because he equally affirms and denies anything at all. And if this man 
takes nothing to be definitely true, and similarly thinks and does not think, just as he similarly 
affirms and denies something in speech, he seems to differ in no way from plants; because 
even brute animals have certain definite conceptions. Another text reads, "from those 
disposed by nature," and this means that such a one who admits nothing does not differ in 
what he is actually thinking from those who are naturally disposed to think but are not yet 
actually thinking. For those who are naturally disposed to think about any question do not 
affirm either part of it, and similarly neither do the others. 

654. It is most evident (349). 

Then he gives a sixth argument, which is based on desire and aversion. In regard to this he 
does two things. First, he gives the argument. Second (350:C 658), he rejects an answer 
which is a quibble ("And if they"). 

He accordingly says, first (349), that it is evident that no man is of such a mind as to think 
that both an affirmation and a negation can be verified of the same subject at the same time. 
Neither those who maintain this position nor any of the others can think in this way. For if to 
go home were the same as not to go home, why would someone go home rather than remain 
where he is, if he were of the opinion that to remain where he is is the same as to go home? 
Therefore, from the fact that someone goes home and does not remain where he is it is clear 
that he thinks that to go and not to go are different. 


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655. Similarly, if someone walks along a path which happens to lead directly to a well or a 
brook, he does not proceed straight along that path but seems to fear that he will fall into the 
well or brook. This happens because he judges that to fall into a well or a brook is not equally 
good and not good, but he judges absolutely that it is not good. However, if he were to judge 
that it is both good and not good, he would not avoid the above act any more than he would 
desire it. Therefore, since he avoids doing this and does not desire it, obviously he judges or 
thinks that the one course is better, namely, not to fall into the well, because fie knows that it 
is better. 

656. And if this is true of what is good and what is not good, the same thing must apply in 
other cases, so that clearly one judges that one thing is a man and another not a man, and that 
one thing is sweet and another not sweet. This is evident from the fact that he does not seek 
all things to the same degree or make the same judgment about them, since he judges that it is 
better to drink water which is sweet than to drink that which is not sweet; and that it is better 
to see a man than to see something which is not a man. And from this difference in opinion it 
follows that he definitely desires the one and not the other; for he would have to desire both 
equally, i.e., both the sweet and the not-sweet, and both man and not-man, if he thought that 
contradictories were the same. But, as has been said before (349:C 655), there is no one who 
does not seem to avoid the one and not the other. So by the very fact that a man is differently 
disposed to various things inasmuch as he avoids some and desires others, he must not think 
that the same thing both is and is not. 

657. It is evident, then that all men think that truth consists in affirmation alone or in negation 
alone and not in both at the same time. And if they do not think that this applies in all cases, 
they at least are of the opinion that it applies in the case of things which are good or evil or of 
those which are better or worse; for this difference accounts for the fact that some things are 
desired and others are avoided. 

658. And if they (350). 

Then he rejects a quibble. For some one could say that men desire some things inasmuch as 
they are good and avoid others inasmuch as they are not good, not because they know the 
truth but because they are of the opinion that the same thing is not both good and not good, 
although this amounts to the same thing in reality. But if it is true that men do not have 
science but opinion, they ought to care all the more about learning the truth. This is made 
clear as follows: one who is ill cares more about health than one who is well. But one who has 
an untrue opinion, in comparison with one who has scientific knowledge, is not healthily 
disposed towards the truth, because he is in the same state with regard to scientific knowledge 
as a sick man is with regard to health; for a false opinion is a lack of scientific knowledge just 
as illness is a lack of health. Thus it is evident that men ought to care about discovering the 
truth. However, this would not be the case if nothing were definitely true, but only if 
something were both true and not true at the same time. 

659. Further, even if all (351). 

Then he gives a seventh argument, which is based on the different degrees of falsity. He says 
that even if it should be most true that everything is so and not so, i.e., that an affirmation and 
its negation are true at the same time, still it is necessary that different degrees of truth should 
exist in reality. For obviously it is not equally true to say that two is even and that three is 
even; nor is it equally false to say that four is five, and that it is a thousand. For if both are 
equally false, it is evident that one is less false, i.e., it is less false to say that four is five than 


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to say that it is a thousand. But what is less false is truer, or nearer to the truth, just as that is 
also less black which is nearer to white. Therefore it is clear that one of them speaks more 
truly, i.e., he comes nearer to the truth; and this is the one who says that four is five. But 
nothing would be closer or nearer to the truth unless there were something which is absolutely 
true in relation to which the nearer or closer would be truer and less false. It follows, then, 
that it is necessary to posit something which is unqualifiedly true, and that not all things are 
both true and false, because otherwise it would follow from this that contradictories are true at 
the same time. And even if it does not follow from the foregoing argument that there is 
something which is unqualifiedly true, still it has been stated already that one thing is truer 
and firmer or more certain than another (351:C 659); and thus affirmation and negation are 
not related in the same way to truth and certitude. Hence as a result of this argument and the 
others given above we shall be freed or liberated from this theory, i.e., from this non-mixed 
opinion, or one that is not tempered (and for this reason another text has "intemperate"); for 
an opinion is well tempered when the predicate is not repugnant to the subject. But when an 
opinion involves opposite notions, it is not well tempered; and the position mentioned above, 
which says that contradictories can be true, is an opinion of this kind. 

660. Further, this position prevents us from being able to define or settle anything in our 
mind. For the first notion of difference is considered in affirmation and negation. Hence he 
who says that an affirmation and a negation are one does away with all definiteness or 
difference. 

661. The doctrine of Protagoras (352). 

Here he shows that the opinion of Protagoras is reduced to the same position as the one 
mentioned above. For Protagoras said that everything which seems to be true to anyone is 
true. And if this position is true, the first one must also be true, namely, that an affirmation 
and its negation are true at the same time. Hence all things must be true and false at the same 
time inasmuch as this follows from this position, as has been shown above (351:C 659). He 
proves this as follows. Many men have opinions which are contrary to one another, and they 
think that those who do not have the same opinions as themselves are wrong, and vice versa. 
If, then, whatever seems so to anyone is true, it follows that both are wrong and both are right, 
because the same thing is and is not. Hence according to the opinion of Protagoras it follows 
that both parts of a contradiction are true at the same time. 

662. Similarly, if it is true that both parts of a contradiction are true at the same time, the 
opinion of Protagoras must be true, namely, that all things which seem true to anybody are 
true. For it is clear that people have different opinions, and some of these are false and others 
are true because they have opinions which are opposed to each other. If, then, all opposites 
are true at the same time (and this follows if contradictories are true at the same time), the 
result must be that all are right, and that what seems so to anyone is true. Thus it is clear that 
each position contains the same opinion, theory, or way of thinking, because one necessarily 
follows from the other. 


LESSON 10 

The Procedure Against Those Who Say that Contradictories Are True at the Same Time 


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ARISTOTLE'S TEXT Chapter 5: 1009a 16-1009a 38 

353. But the same method of discussion is not applicable in all of these cases, because some 
men need persuasion and others force. For the ignorance of those who have formed their 
opinions as a result of difficulties is easily cured, because refutation is directed not against 
their words but against their thought. But the cure for all of those who argue for the sake of 
argument consists in refuting what they express in speech and in words. 

354. Those who have experienced difficulties have formed this opinion because of things 
observed in the sensible world, i.e., the opinion that contradictories and contraries can both be 
true at the same time, inasmuch as they see that contraries are generated from the same thing. 
Therefore, if it is impossible for nonbeing to come into being, the thing must have existed 
before as both contraries equally. This is Anaxagoras' view, for he says that everything is 
mixed in everything else. And Democritus is of the same opinion, for he holds that the void 
and the full are equally present in any part, and yet one of these is non-being and the other 
being. 

355. Concerning those who base their opinions on these grounds, then, we say that in one 
sense they speak the truth, and that in another they do not know what they are saying. For 
being has two meanings, so that in one sense a thing can come to be from non-being and in 
another sense it cannot. Hence the same thing can both be and not be at the same time, but not 
in the same respect; for while the same thing can be potentially two contraries at the same 
time, it cannot in complete actuality. 

356. Further, we shall expect them to believe that among beings there is also another kind of 
substance to which neither motion nor generation nor corruption belongs in any way. 

COMMENTARY 

663. Having raised arguments against those who deny the first principle, and having settled 
the issue, here the Philosopher indicates how one must proceed differently against various 
men who adopted different versions of the above-mentioned error. This is divided into two 
parts. 

In the first (353 :C 663) he shows that one must proceed differently against different men. In 
the second (354:C 665) he begins to proceed in a different way than he did above ("Those 
who"). 

He accordingly says, first (353), that the same method "of discussion," i.e., of popular address 
(or "of good grammatical construction," according to another translation, or of well ordered 
argument "or intercession," as is said in the Greek, i.e., of persuasion) is not applicable to all 
of the foregoing positions; that is, to the position that contradictories can be true, and to the 
position that truth consists in appearances. For some thinkers adopt the foregoing positions 
for two reasons. Some do so because of some difficulty; for since certain sophistical 
arguments occur to them, from which the foregoing positions seem to follow, and they do not 
know how to solve them, they accept the conclusion. Hence their ignorance is easily cured. 
For one must not oppose them or attack the arguments which they give, but must appeal to 
their thought, clearing up the mental difficulties which have led them to form such opinions; 
and then they will give up these positions. 


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664. Others adopt the foregoing positions, not because of any difficulty which leads them to 
such positions, but only because they want to argue "for the sake of argument," i.e., because 
of a certain insolence, inasmuch as they want to maintain impossible theories of this kind for 
their own sake since the contrary of these cannot be demonstrated. The cure for these men is 
the refutation or rejection "of what they express in speech and in words," i.e., on the grounds 
that the word in a statement has some meaning. Now the meaning of a statement depends on 
the meaning of the words, so that it is necessary to return to the principle that words signify 
something. This is the principle which the Philosopher used above (332:C 611). 

665. Those who (354). 

Since the Philosopher met the difficulties above on this point by considering the meaning of 
words, he begins here to meet those who are in difficulties by solving their problems. 

First (354), he deals with those who held that contradictories are true at the same time; and 
second (357:C 669), he deals with those who held that everything which appears so is true 
("And similarly"). 

In regard to the first he does two things. First, he sets forth the difficulty which led some men 
to admit that contradictories are true at the same time. Second (355 :C 667), he clears up this 
difficulty ("Concerning those"). 

He says, then, that the opinion on this point, that the parts of a contradiction may be true at 
the same time, was formed by some men as a result of a difficulty which arose with regard to 
sensible things, in which generation and corruption and motion are apparent. For it seemed 
that contraries were generated from the same thing; for example, air, which is warm, and 
earth, which is cold, both come from water. But everything which is generated comes from 
something that existed before; for non-being cannot come into being, since nothing comes 
from nothing. A thing therefore had to have in itself contradictories simultaneously, because 
if both the hot and the cold are generated from one and the same thing, then it turns out to be 
hot and not-hot itself. 

666. It was because of such reasoning that Anaxagoras claimed that everything is mixed in 
everything else. For from the fact that anything at A seemed to come from anything else he 
thought that one thing could come from another only if it already existed in it. Democritus 
also seems to have agreed with this theory, for he claimed that the void and the full are 
combined in any part of a body. And these are like being and non-being, because the full has 
the character of being and the void the character of non-being. 

667. Concerning those (355). 

Here he solves the foregoing difficulty in two ways. First, he says that the opinion of those 
who have adopted the foregoing absurd views because of some difficulty must be met by 
appealing to their thought, as has been stated (353 :C 663). Therefore "concerning those who 
base their opinions," i.e., those who think that contradictories are true at the same time, "on 
these grounds," i.e., on the reasoning mentioned above, we say that in one sense they speak 
the truth and in another they do not know what they are saying since their statements are 
absurd. For being has two meanings: actual being and potential being; and therefore when 
they say that being does not come from non-being, in one sense they are right and in another 
they are not. For being does not come from actual being but from potential being. Hence in 
one sense the same thing can be at the same time both being and non-being, and in another 


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sense it cannot; for the same thing can be contraries potentially, but it cannot be both "in 
complete actuality," i.e., actually. For if something warm is potentially both hot and cold, it 
still cannot be actually both. 

668. Further, we shall (356). 

Then he gives the second solution. He says that we deem it fitting that they should accept or 
think that there is some kind of substance to which neither motion nor generation nor 
corruption belongs, as is proved in Book VIII of the Physics. Now one could not conclude to 
the existence of this kind of substance by reason of what has been said above, namely, that 
contraries belong to it, because nothing is generated from them. This solution seems to be like 
the one reached by the Platonists, who, because of the changeable character of sensible 
things, were compelled to posit unchangeable separate Forms (i.e., those of which definitions 
are given, and demonstrations made, and certain knowledge is had) on the grounds that there 
could be no certain knowledge of sensible things because of their changeableness and the 
mixture of contrariety which they contain. But the first solution is a better one. 


LESSON 11 

The Reason Why Some Considered Appearances to Be True 
ARISTOTLE'S TEXT Chapter 5: 1009a 38-100% 12 

357. And similarly the theory that truth consists in appearances comes to some thinkers from 
sensible things. For they think that the truth should not be judged by the large or small 
number who uphold some view; and they point out that the same thing appears to be sweet to 
some when they taste it and bitter to others. Hence, if all men were ill or all were mad, and 
only two or three were healthy or in possession of their wits, the latter would appear ill or 
mad and not the former. Further, they say that the impressions made upon many of the other 
animals are contrary to those made upon us, and that to the senses of each person things do 
not always appear to be the same. Therefore it is not always evident which of these views is 
true or which is false, but both appear equally so. And it is for this reason that Democritus 
says that either nothing is true or it is not evident to us. 

COMMENTARY 

669. Having solved the difficulty which led the ancient philosophers to maintain that 
contradictories are true at the same time, the Philosopher now dispels the difficulty which led 
some thinkers to maintain that every appearance is true. 

This part is divided into two. First (351:C 669), he gives the difficulties which led some 
thinkers to hold the position mentioned above. Second (363 :C 685), he dispels these 
difficulties ("But in reply"). 

In regard to the first he does two things. First, he gives the reason which led these men to 
maintain that every appearance is true. Second (358:C 672), he explains why they reasoned in 
this way ("In general"). 


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He therefore says, first (357), that, just as the opinion which maintained that contradictories 
are true at the same time came from certain sensible things in which it happens that 
contradictories come from the same thing, so too "the theory that truth consists in 
appearances," or the opinion about the truth of appearances, is derived from certain sensible 
things; that is, by those who are not perverse but are drawn into this position because of 
difficulties. This occurs because they find that different men hold contrary opinions about the 
same sensible things; and they give three reasons in support of their position. First, they point 
out that the same thing appears to taste sweet to some atid bitter to others, so that men have 
contrary opinions about all sensible things. Second, they note that many animals make 
judgments about sensible things which are contrary to ours; for what seems tasty to the ox or 
to the ass is judged by man to be unpalatable. Third, they say that the same man at different 
times makes different judgments about sensible things; for what now appears to be sweet and 
palatable to him at another time seems bitter or tasteless. 

670. And no certain reason can be given that clearly indicates which of these opinions is true 
or which is false, because one of these seems no truer to one person than the other does to 
another person. Therefore they must be equally true or equally false. Hence Democritus said 
that either nothing is definitely true or, if anything is true, it is not evident to us; for even 
though we acquire our knowledge of things through the senses, their judgment is not certain 
since they do not always judge in the same way. Hence we do not seem to have any certainty 
regarding the truth so that we can say that this opinion is definitely true and its contrary 
definitely false. 

671. But someone could say, in opposing this position, that some rule can be adopted 
whereby a person can discern among contrary opinions the one that is true. That is, we might 
say that the judgment which healthy people make about sensible things is right, and the one 
which sick people make is not; and that the judgment which wise and intelligent people make 
in matters of truth is right, and the one which foolish or ignorant people make is not. He 
rejects this reply at the very start on the grounds that no certain judgment about the truth of 
any theory can be fittingly based on the number, large or small, of persons who hold it, 
according to which that would be said to be true which seems so to many, and that to be false 
which seems so to a few; for sometimes what many believe is not simply true. Now health 
and sickness or wisdom and foolishness do not seem to diff er only by reason of the greater or 
smaller number of people involved. For if all or most persons were like those who are now 
thought to be ignorant or foolish, they would be considered wise, and those who are now 
thought to be wise would be considered foolish. The same applies in the case of health and 
sickness. Hence the judgment regarding truth and falsity of one who is healthy and wise is no 
more credible than the judgment of one who is ill and foolish. 


LESSON 12 

Two Reasons Why Some Identify Truth with Appearances 
ARISTOTLE'S TEXT Chapter 5: 1009b 12-1010a 15 

358. And in general it is because these philosophers think that discretion is sensory 
perception, and that this in turn is alteration, that they say that what appears to the senses is 
necessarily true. 


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359. For it is for these reasons that both Empedocles and Democritus and, we may probably 
say, every one of the other philosophers became involved in such opinions. For Empedocles 
also says that when men change their condition they change their knowledge, "for 
understanding varies in men in relation to what is seen," according to him. And elsewhere he 
says, "Insofar as they are changed into a different nature, to that extent it is proper for them 
always to think other thoughts." And Parmenides also speaks in the same way: "For just as 
each has his mixture of many-jointed limbs, so intellect is present in men; for it is the same 
thing, the nature of the limbs, which exercises discretion in men — in all and in each; for that 
which is more is intellect." Anaxagoras is also recorded as saying to some of his companions 
that things were such to them as they thought them to be. And men also say that Homer 
maintained this view, because he made Hector, after he was stunned by the blow, think other 
thoughts; implying that people of sound and unsound mind both think but not the same 
thoughts. It is evident, then, that if both of these states of mind are forms of knowledge, 
beings must also be so and not so at the same time. 

360. Hence their conclusion happens to be the most serious one. For if those who have seen 
most clearly the truth which it is possible for us to have (and these are those who seek and 
love it most), maintain such opinions and express such views about the truth, how is it 
unfitting that those who are trying to philosophize should abandon the attempt? For to seek 
the truth will be like chasing birds. 

361. Now the reason these men held this opinion is that, while they investigated the truth 
about beings, they thought that sensible things alone exist; and in these much of the nature of 
the indeterminate, i.e., the kind of being which we have described (355), is present. Hence, 
while they speak in a plausible way, they do not say what is true; for it is more plausible to 
speak as they do than as Epicharmus did to Xenophanes. 

362. Again, since they saw that the whole of the natural world is in motion, and that we can 
say nothing true about what is undergoing change, they came to the conclusion that it is 
impossible to say anything true about what is always changing altogether. For it was from this 
view that the most extreme of the opinions mentioned above blossomed forth; that is, the 
opinion held by those who are said to Heraclitize, and such as Cratylus expressed, who finally 
thought that he should say nothing but only moved his finger, and criticized Heraclitus for 
saying that it is impossible to step into the same river twice; for he himself thought that this 
could not be done even once. 

COMMENTARY 

672. He gives the reason why these philosophers adopted the foregoing position. First (358:C 
672), he shows how sensory perception provided one reason for adopting this position; and 
second (361 :C 681), how sensible objects provided another ("Now the reason"). 

In regard to the first part he does three things. First, he explains how sensory perception 
provided one reason for adopting this position. Second (359:C 674), he recounts the opinions 
of different men which have this reason as their common basis ("For it is"). Third (36o:C 
680), he attacks these opinions ("Hence their conclusion"). 

He accordingly says, first (158), that the ancients were of the opinion that discretion, i.e., 
wisdom or science, is merely sensory perception; for they did not make any distinction 
between sense and intellect. Now sensory perception comes about through a certain alteration 
of a sense with reference to sensible objects. And so the fact that a sense perceives something 


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results from the impression which a sensible thing makes on the sense. Thus a sensory 
perception always corresponds to the nature of the sensible object as it appears. Hence, 
according to these thinkers, whatever appears to the senses is necessarily true; and since we 
must add that all knowing is sensory, it follows that whatever appears in any way at all to 
anyone is true., 

673. But this argument fails, not only because it holds that sense and intellect are the same, 
but also because it maintains that the judgment which a sense makes about sensible objects is 
never false. For while a sense may make a mistake about common and accidental sensible 
objects, it does not do this with regard to its proper sensible object, except perhaps when the 
sensory organ is indisposed. And even though a sense is altered by its sensible object, the 
judgment of a sense does not have to conform to the conditions of the sensible object; for it is 
not necessary that the action of an agent be received in the patient according to the mode of 
being of the agent but only according to that of the patient or subject. This is why a sense 
sometimes is not disposed to receive the form of a sensible object according to the mode of 
being which the form has in the sensible object, and it therefore sometimes judges a thing to 
be otherwise than it really is. 

674. For it is (359). 

He presents the opinions which different men held for the reasons stated above. Now all of 
the statements of these men which he adduces imply two things: first, that intellect is the 
same as sense, and, second, that every appearance is true. Thus he says that it is for the 
reasons mentioned above that Empedocles and Democritus and each of the other philosophers 
became involved in such opinions about reality "we may probably say," i.e., we can 
conjecture on the basis of their statements. 

675. For Empedocles said that those who change "their condition," i.e., some bodily 
disposition, also change their understanding; implying that the intellect, to which knowledge 
belongs, depends on a condition of the body, just as a sense does. For understanding increases 
in men "in relation to what is seen"; that is, an increase in knowledge takes place in a man by 
reason of the fact that something new begins to appear to him, and this comes about as a 
result of some change in a bodily disposition. Another translation states this more clearly, 
saying, "For purpose or decision develops in man in relation to what is at hand"; as if to say, 
according to the different dispositions which are actually present in men, new decisions or 
new purposes or new judgments develop in them. And the implication is that decision or 
purpose does not, depend on any intellective power in man over and above the senses but 
only on a disposition of the body, which is changed with the presence of different things. But 
in other works ' of his Empedocles says that, to the extent that alteration occurs, that is, to the 
extent that men are changed to another bodily disposition, to that extent, he says, there is 
always thoughtfulness in them; that is, thought, concern, or planning arises in them 
proportionately. This translation is a difficult one to understand, but another states this notion 
more clearly, saying, "to the extent that men have been changed, to that extent they are 
always determined to think other thoughts or even foolish ones." Or according to another text, 
"It is proper for them [always to think other thoughts]," as if to say that, insofar as a man is 
changed in some bodily disposition, to that extent his basic outlook is different-implying that 
he has a different understanding and a different outlook. 

676. Then he gives Parmenides' opinion in this matter. He says that Parmenides speaks about 
the truth of things in the same way that Empedocles does, for Parmenides says ' that, just as 
each man has an arrangement of jointed members, or "of many-jointed limbs," according to 


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another text, so intellect is present in men; implying that there is a great deal of variety and 
circumvolution in the members of man in order that such an arrangement of members may be 
adjusted for the operation of the intellect, which depends on the way in which the members 
are combined, according to him. For he says that it is the same thing "which cares for," i.e., 
which has the care or supervision of the members because of the nature of the members, and 
which is "in each," i.e., in the individual parts of the universe, and "in all," i.e., in the whole 
universe. Yet insofar as it is present in the whole universe and in its individual parts and in 
men, it is designated by different names. In the whole universe it is called God, in the 
individual parts it is called nature, and in men it is called thought. Thus it is present to a 
greater degree in man than it is in the other parts of the universe; for in man this power thinks 
as a result of the determinate way in which his members are combined, but this does not apply 
in the case of other things. In this statement he also wants it understood that thought is a result 
of the way in which the body is composed, and thus does not differ from sensory perception. 
Another translation states this more clearly, saying, "For it is the same thing, the nature of the 
limbs, which exercises discretion in men-in all and in each; for that which is more is 
intellect." 

677. Then he gives the opinion of Anaxagoras, who expressed it to some of his companions 
and friends and had them commit it to memory, namely, that things are such to them as they 
take or believe them to be. This is the second point which is touched on in these statements of 
the philosophers, namely, that truth depends on opinion. 

678. Then he gives the view of Homer, who seemed to be of the same opinion according to 
what people said of him. For in his story he made Hector lie, as it were, in a trance from the 
blow which he had been dealt, "lingering in another place," i.e., to think other thoughts than 
he had thought before, or, according to another text, to be of a different opinion from the one 
which he had before; as if in lingering and not lingering, i.e., in the state in which he lay after 
being struck down, he would both think and not think, although not about the same thing. For 
he knew those things which then appeared to him, but not those which he had known before, 
and had then ceased to know. Another translation expresses the idea thus: "Implying that 
people of sound and unsound mind both think but not the same thoughts"; as if to say that, 
just as this is true of Hector, who had strange opinions after the blow, so too it is possible for 
others to have sound and foolish opinions at the same, although not about the same things but 
about different ones. 

679. Now from all of the foregoing views of the philosophers he draws his intended 
conclusion that, if both of these states of mind constitute knowledge, i.e., those states in 
which a man thinks contrary things when he is changed from one state to another, it follows 
that whatever anyone thinks is true; for knowing would not consist in thinking what is false. 
Hence it follows that beings are equally so and not so. 

680. Hence, their conclusion (360). 

Here he attacks the above-mentioned philosophers. He says that the conclusion which they 
drew is the most serious one. For if those who have seen the truth most clearly, insofar as it is 
possible for man to see it (namely, the foregoing philosophers, who are also the ones that love 
and seek it most of all) offer such opinions and views about the truth, how is it unfitting that 
these philosophers should grieve about the ineffectualness of their study if truth cannot be 
found? Another text reads, "How is it unfitting that those who are trying to philosophize 
should give up or abandon the attempt?" i.e., that a man should not cling to those who want to 
philosophize but despise them. For, if a man can know nothing about the truth, to seek the 


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truth is to seek something which he cannot attain. In fact he resembles someone who chases 
or hunts birds; for the more he pursues them the farther they get away from him. 

681. Now the reason (361). 

He indicates how sensible things influenced this opinion, i.e., how they provided a basis for 
the above-mentioned position. For, since sensible things are naturally prior to the senses, the 
dispositions of the senses must depend on those of sensible things. He gives two ways in 
which sensible things provided a basis for this position. The second (362) is treated at the 
words, "Again, since they." 

He accordingly says, first, that the reason why the foregoing philosophers adopted this 
position is this: since they aimed to know the truth about beings, and it seemed to them that 
sensible things alone exist, they therefore based their doctrine about truth in general on the 
nature of sensible things. Now in sensible things much of the nature of the infinite or 
indeterminate is present, because they contain matter, which is not in itself limited to one 
form but is in potency to many; and in these the nature of being is also found just as we have 
pointed out: the being of sensible things is not determinate but is open to various 
determinations. It is not to be wondered at, then, if he does not assign a definite knowledge to 
the senses, but one kind of knowledge to one sense, and another kind to another sense. 

682. And for this reason the abovementioned philosophers use the foregoing argument 
plausibly or fittingly, though they are not right in claiming that there is nothing definite in 
sensible things; for even though matter in itself is indeterminately disposed for many forms, 
nevertheless by a form it is, determined to one mode of being. Hence, since things are known 
by their form rather than by their matter, it is wrong to say that we can have no definite 
knowledge of them. Yet, since the opinion of these philosophers has some plausibility, it is 
more fitting to speak as they do than as Epicharmus did to Xenophanes, who seems to have 
said that all things are immovable, necessary and known with certainty. 

683. Again, since they (362). 

He gives the second way in which sensible things provided a basis for this opinion. He says 
that the philosophers saw that the whole of the natural world, i.e., the sensible world, is in 
motion, and they also saw that no attribute can be predicated of anything that is being 
changed insofar as it is being changed; for whatever is being changed insofar as it is being 
changed is neither white nor black. Hence, if the nature of sensible things is being changed 
always and "altogether," i.e., in all respects, so that there is nothing fixed in reality, it is 
impossible to make any statement about them that is definitely true. Thus it follows that the 
truth of an opinion or proposition does not depend on some determinate mode of being in 
reality but rather on what appears to the knower; so that it is what appears to each individual 
that is true for him. 

684. That such was their argument becomes clear as follows. For from this assumption or 
opinion there sprouted "the most serious or extreme" opinion of the philosophers of whom we 
have spoken, i.e., the opinion which is found to be the most serious or extreme in this class. 
And this is the one which he called "Heraclitizing," i.e., following the opinion of Heraclitus, 
or the opinion of those who were disciples of Heraclitus, according to another text, or of those 
who professed to follow the opinion of Heraclitus, who claimed that all things are in motion 
and consequently that nothing is definitely true. This opinion also was maintained by 
Cratylus, who finally arrived at such a pitch of madness that he thought that he should not 


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express anything in words, but in order to express what he wanted he would only move his 
finger. He did this because he believed that the truth of the thing which he wanted to express 
would pass away before he had finished speaking. But he could move his finger in a shorter 
space of time. This same Cratylus also reprimanded or rebuked Heraclitus. For Heraclitus 
said that a man cannot step into the same river twice, because before he steps in a second time 
the water of the river already has flowed by. But Cratylus thought that a man cannot step into 
the same river even once, because even before he steps in once the water then in the river 
flows by and other water replaces it. Thus a man is incapable not only of speaking twice 
about anything before his disposition is changed but even of speaking once. 


LESSON 13 

Change in Sensible Things Not Opposed to Their Truth 
ARISTOTLE'S TEXT Chapter 5: 1010a 15-1010b 1 

363. But in reply to this theory we shall also say that there is some reason why these men 
should think that what is changing, when it is changing, does not exist. 

364. Yet there is a problem here; for what is casting off some quality retains something of 
what is being cast off, and something of what is coming to be must already exist. And in 
general if a thing is ceasing to be, there must be something which is; and if a thing is coming 
to be, there must be something from which it comes to be and something by which it comes to 
be; and this process cannot proceed to infinity. 

365. But setting aside these considerations, let us say that change in quantity and change in 
quality are not the same. Let it be granted, then, that a thing does not remain the same in 
quantity; but it is by reason of its form that we know each thing. 

366. Again, those who hold this view deserve to be criticized, because what they saw in the 
case of a very small number of sensible things they asserted to be true also of the whole 
universe. For it is only that region of the sensible world about us which is always in process 
of generation and corruption. But this is, so to speak, not even a part of the whole, so that it 
would have been juster for them to have esteemed the changing because of the whole than to 
misjudge as they did the whole because of its changing part. 

367. Further, it is evident that in answering these men we shall say the same things as we said 
before (356); for we must show them and make them understand that there is a kind of nature 
which is immobile. 

368. And those who say that the same thing both is and is not at the same time can also say 
that all things are at rest rather than in motion. For according to this view there is nothing into 
which anything may be changed, since everything is already present in everything. 

COMMENTARY 

685. He argues against the foregoing opinions. First (363:C 685), he argues against the views 
that were held about the changeable character of sensible things; and second (369:C 692), 


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against the statements that were made regarding sensory appearances ("Now concerning the 
truth"). 

In regard to the first part (363) he gives six arguments. The first of these is as follows: he who 
thinks that what is not does not exist, has a true opinion and makes a true statement if he 
expresses this. But what is being changed, while it is being changed, is neither that to which it 
is being changed nor that from which it is being changed; and thus some true statement can be 
made about a thing that is undergoing change. Hence, in opposing the foregoing theory or 
"account" (i.e., the opinion that no true statement can be made about anything which is 
changing), we can say that there is some ground or valid reason "in their case," i.e., according 
to the opinion of the foregoing philosophers, for thinking "that what is changing," or what is 
being changed, "when it is changing," i.e., while it is undergoing change, does not exist; that 
is, there is some reason for thinking that it has no being. 

686. Yet there is (364). 

Then he gives the second argument, and it runs thus: everything which is being changed 
already has some part of the terminus to which it is being changed, because what is being 
changed, while it is being changed, is partly in the terminus to which it is being changed, and 
partly in the terminus from which it is being changed, as is proved in Book VI of the Physics 
(or, according to another text, "that which is casting off some quality retains sdmething of 
what is being cast off). And by this statement we are given to understand that anything 
which is being moved retains some part of the terminus from which it is being moved, 
because so long as a thing is being moved it is casting off the terminus from which it is being 
moved; and it is possible only to cast off some quality which belongs to a mobile subject. And 
something of what is coming to be must already exist, because everything which is coming to 
be was coming to be, as is proved in Book VI of the Physics. And it is also evident that, if 
something is ceasing to be, there must be something which is; for if it did not exist in any way 
at all, it already would have ceased to be and would not be ceasing to be. Similarly, if 
something is coming to be, there must be a matter from which it is coming to be and an agent 
by which it is coming to be. But this cannot go on to infinity, because, as is proved in Book II 
(153:C 301), there cannot be an infinite regress either in the case of material causes or in that 
of efficient causes. Hence a major problem faces those who say that no true statement can be 
made about anything which is being moved or generated, both because each thing which is 
being moved or generated has some part of the terminus to which it is being moved, and 
because in every process of generation or motion there must be held to be something 
unproduced and unchangeable both on the part of the matter and on that of the agent. 

687. But setting aside (365). 

Then he gives the third argument, and this rejects the very ground on which these thinkers 
base their opinion that all sensible things are always in motion. For they were led to make this 
statement because of things which increase as a result of growth. For they saw that a thing 
increases in quantity to a very small degree during one year, and they thought that the motion 
of growth was continuous, so that quantity, in which increase is observed, might be divided in 
proportion to the parts of time. Thus an increase in some part of quantity would take place in 
some part of time, and this part of quantity would be related to a whole quantity as some part 
of a period of time to the whole of that period. And since this kind of motion is imperceptible, 
they also thought that things which appear to be at rest are being moved, although by an 
imperceptible motion. 


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688. In opposing these thinkers, then, he says that, even apart from the considerations which 
have been made, it is clear that change in quantity and in quality or form are not the same. 
And although they admit that change in quantity is continuous in reality, and that all things 
are always being moved imperceptibly by this motion, it is not therefore necessary for this 
reason that all things should be being moved in quality or form. Hence it will be possible to 
have a definite knowledge of things, because things are known by their form rather than by 
their quantity. 

689. Again, those who (366). 

Then he gives the fourth argument. He says that "those who think in this way,',' i.e., those 
who entertain the opinion that all sensible things are always being moved because they find a 
small number of sensible things of which this is true, deserve to be criticized; for there are 
many sensible things which are capable, of being moved only from the viewpoint of local 
motion. For it is obvious that it is only the sensible things around us here in the sphere of 
active and passive things which are in process of generation and corruption. But this sphere or 
place amounts to nothing, so to speak, in comparison with the whole universe; for the entire 
earth has no sensible quantity in comparison with the outermost sphere. Hence this place is 
related to the universe as its central point, as the astronomers prove on the grounds that the six 
signs of the zodiac always appear above the earth. But this would not be the case if the earth 
were to hide from us some part of the heavens which are perceived by the senses. For it 
would be foolish to make a judgment about the whole sensible world in the light of these few 
things. Indeed, it would have been more acceptable if the whole sensible world had been 
judged according to the motion of the celestial bodies, which far surpass the others in 
quantity. 

690. Further, it is evident (367). 

He gives the fifth argument. He says that we must also use the same arguments against these 
men as were used above in this same book; that is, we must show them that there is a kind of 
nature which is immobile, namely, that of the primary mover, as is proved in Book VIII of the 
Physics. And this argument must be used against them, and they ought to accept it, as has 
been proved elsewhere (356:C 668). It is not true, then, that all things are always in motion, 
and that it is impossible to make any true statement about anything. 

691. And those who say (368). 

He gives the sixth argument. He says that their position that all things are being moved is 
opposed to their first position, that contradictories are true of the same subject at the same 
time, because if something is and is not at the same time, it follows that all things are at rest 
rather than in motion. For nothing is being changed in terms of any attribute which already 
belongs to it; for example, what is already white is not being changed as regards whiteness. 
But if it is possible for the same thing both to be and not be at the same time, all attributes 
will be present in all things, as has been proved above (345 :C 639), because all will be one. 
Hence there will not be anything to which a thing can be changed. 


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Seven Arguments against the View that Truth Consists in Appearances 

ARISTOTLE'S TEXT Chapter 5: 1010b l-1011a 2 

369. Now concerning the truth that not everything which appears is true, the following points 
must be taken into consideration: first, that a sense is not false with regard to its proper object, 
but imagination is not the same as a sense. 

370. Second, that it is surprising if some should raise the question whether continuous 
quantities are as great and colors really such as they appear to those who are at a distance or 
as they appear to those who are close at hand, and whether things are such as they appear to 
those who are healthy or to those who are ailing, and whether heavy things are such as they 
appear to those who are weak or to those who are strong, and whether those things are true 
which appear to those who are asleep or to those who are awake. For it is clear that they do 
not think so. Therefore no one who is in Lybia, having dreamed that he was in Athens, would 
go to the Odeon. 

371. Again, concerning future things, as Plato says, the opinion of a physician and that of a 
person who is ignorant of the art of medicine are not of equal value as to whether someone 
will get well or not. 

372. Again, in the case of the senses the perception of a foreign object and that of a proper 
object, or that of a kindred object and that of the object of the sense concerned, are not of 
equal value. In the case of colors it is sight and not taste which passes judgment; and in the 
case of flavors it is taste and not sight which does this. 

373. And no one of these senses ever affirms at the same time about the same subject that it is 
simultaneously both so and not so. Nor at another time does it experience any difficulty about 
a modification, but only about the object of which the modification is an accident. I mean, for 
example, that the same wine, either as a result of a change in itself or in the body, might seem 
at one time sweet and at another not, But sweetness, such as it is when it exists, has never 
changed; but one is always right about it, and sweetness itself is necessarily such as it is. 

374. Yet all these theories destroy this, for just as things will have no substance, neither will 
they have any necessity; for that is necessary which cannot be in one way and in another. 
Hence, if anything is necessary, it will not be both so and not so. 

375. And in general if only the sensible actually exists, there would be nothing if living things 
did not exist; for there would be no senses. Therefore the position that neither sensible objects 
nor sensory perceptions would exist is perhaps true, for these are modifications of the one 
sensing. But that the underlying subjects which cause perception should not exist apart from 
perception is impossible; for a perceptioii is not the perception of itself, but there is some 
other 

thing besides the perception which must be prior to the perception. For that which causes 
motion is naturally prior to that which is moved, and this is no less true if they are correlative 
terms. 

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692. Here he begins to argue dialectically against the opinion that truth if equivalent to 
appearances; and in regard to this he does two things. First (369:C 718), he rejects this 
opinion. Second (381:C 718), he draws his intended conclusion ("Let this suffice"). 

In regard to the first he does two things. First, he argues dialectically against those who held 
this opinion because of some theory or difficulty. Second (376:C 708), he argues against 
those who held this opinion because of insolence ("Now there are some"). 

In regard to the first part (369) he gives seven arguments. The first of these is as follows: it 
has been shown (367:C 690) that not all things are changeable, and "concerning the truth that 
not everything which appears is true," these points must be considered. First, the proper cause 
of falsity is not the senses but the imagination, which is not the same as the senses. That is to 
say, the diversity of judgments made about sensible objects is not attributable to the senses 
but to the imagination, in which errors are made about sensory perceptions because of some 
natural obstacle. Now imagination is not the same as perception, as is proved in Book III of 
The Soul, but is a motion produced as a result of actual sensing. Therefore in attributing to the 
senses this diversity of judgments by which one person is considered to have a false 
perception of a particular object about which another has a true perception, they do not 
proceed as they should. Another translation states this better, saying, "And, first, it must be 
understood that a sense is not false with regard to its proper object," implying that no sense 
makes a mistake about its own proper object; for example, sight is not mistaken about colors. 
From this it is evident that the judgment which a sense makes about its proper sensible object 
is a definite one, so that there must be some definite truth in the world. 

693. And if someone raises the objection that error sometimes arises even with regard to 
proper sensibles, his answer is that this is attributable not to the senses but to the imagination; 
for when the imagination is subject to some sort of abnormality, it sometimes happens that the 
object apprehended by a sense enters the imagination in a different way than it was 
apprehended by the sense. This is evident, for example, in the case of madmen, in whom the 
organ of imagination has been injured. 

694. Second, that it is (370). 

Then he gives his second argument, and it runs thus: it is surprising if some "should raise the 
question," or "be puzzled," as another text says, whether continuous quantities are such as 
they appear to those who are at a distance or to those who are close at hand. For it is just 
about self-evidently true that a sense judges quantities which are close at hand to be such as 
they are, and those which are far away to be smaller than they are, because what seems farther 
away appears small, as is proved in the science of optics. 

695. The same thing applies if someone raises the question whether colors are such as they 
appear to those who are close at hand; for it is evident that the farther an agent's power is 
extended when it acts, the more imperfect is its effect; for fire heats those things which are far 
away to a lesser degree than those which are close at hand. And for the same reason the color 
of a perfect sensible body does not change that part of the transparent medium which is far 
away from it as completely as it changes that part which is close to it. Hence the judgment of 
a sense is truer about sensible colors in things close at hand than it is about those in things far 
away. 

696. The same thing is also true if someone asks whether things are such as they appear to 
those who are healthy or "to those who are ailing," i.e., those who are ill. For healthy people 


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have sensory organs which are well disposed, and therefore the forms of sensible things are 
received in them just as they are; and for this reason the judgment which healthy people make 
about sensible objects is a true one. But the organs of sick people are not properly disposed, 
and therefore they are not changed as they should be by sensible objects. Hence their 
judgment about such objects is not a true one. This is clear with regard to the sense of taste; 
for when the organ of taste in sick people has been rendered inoperative as a result of the 
humors being destroyed, things which have a good taste seem tasteless to them. 

697. The same thing also applies regarding the question whether things having weight are as 
heavy as they seem to those who are weak or to those who are strong; for it is clear that the 
strong judge about heavy things as they really arc. But this is not the case with the weak, who 
find it difficult to lift a weight not only because of the heaviness of it (and this sometimes 
happens even with the strong) but also because of the weakness of their power, so that even 
less heavy things appear heavy to them. 

698. The same thing again applies if the question is raised whether the truth is such as it 
appears to those who are asleep or to those who are awake. For the senses of those who are 
asleep are fettered, and thus their judgment about sensible things cannot be free like the 
judgment of those who are awake and whose senses are unfettered. For it has been pointed 
out above that it would be surprising if they should be perplexed, because it appears from 
their actions that they are not perplexed, and that they do not think that all of the 
above-mentioned judgments are equally true. For if someone in Lybia seems in his dreams to 
be in Athens, or if someone in Paris seems in his dreams to be in Hungary, he does not when 
he awakens act in the same way that he would if he were to perceive this when he is awake. 
For, if he were awake in Athens, he would go to the Odeon, i.e., a building in Athens; but he 
would not do this if he had merely dreamed it. It is clear, then, that he does not think that 
what appears to him when he is asleep and what appears when he is awake are equally true. 

699. We can argue in the same way with regard to the other issues mentioned above; for even 
though men often raise questions about these issues, they are not in their own mind perplexed 
about them. Hence it is clear that their reason for holding to be true everything which appears, 
is invalid; for they held this position because of the impossibility of deciding which of several 
opinions is the truer, as has been stated above (353 :C 663). 

700. Again, concerning future (371). 

Here he gives his third argument. He says that in the case of future events, as Plato points out, 
the opinion of a physician and that of a person who is ignorant of the art of medicine are not 
"of equal value," i.e., equally important, certain, true or acceptable, as to the future possibility 
of some sick person being cured or not. For, while a physician knows the cause of health, this 
is unknown to someone who is ignorant of the art of medicine. It is clear, then, that the 
opinion which some held that all opinions are equally true is a foolish one. 

701. Again, in the case (372). 

He gives his fourth argument, which runs thus: in the case of sensible objects the judgment 
which a sense makes about some sensible object foreign to it and that which it makes about 
its proper sensible object are not of equal "value," i.e., equally true and acceptable; for 
example, sight and taste do not make the same sort of judgment about colors and flavors, but 
in the case of colors the judgment of sight must be accepted, "and in the case of flavors," or 
savors, the judgment of taste must be accepted. Hence, if sight judges a thing to be sweet and 


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taste judges it to be bitter, taste must be accepted rather than sight. 

702. And in the same way too the judgment which a sense makes about its proper sensible 
object and the one which it makes about something akin to its proper object are not of equal 
value. Now those things which are said here to be akin to proper sensible objects are called 
common sensibles, for example, size, number and the like, about which a sense is deceived to 
a greater degree than it is about its proper sensible object, although it is deceived about them 
to a lesser degree than it is about the sensible objects of another sense or about things which 
are called accidental sensible objects. Hence it is clearly foolish to say that all judgments are 
equally true. 

703. And no one (373). 

He now gives his fifth argument. He says that no sense affirms at one instant of time that a 
thing is simultaneously both so and not so. For sight does not at the same moment affirm that 
something is white and not white or that it is two cubits and not two cubits or that it is sweet 
and not sweet. But while a sense's power of judging may seem at different times to form 
opposite judgments about the same thing, still from this judgment no difficulty ever arises 
about the sensible modification itself, but only about the subject of this modification. For 
example, if we take the same subject, wine, sometimes it appears to the sense to taste sweet 
and sometimes not. This happens either because of some change in the sentient body, i.e., in 
the organ, which is infected by bitter humors, so that whatever it tastes does not seem sweet 
to it, or else because of some change in the wine itself. But the sense of taste never changes 
its judgment without judging sweetness itself to be such as it considered it to be in the sweet 
thing when it judged it to be sweet; but about sweetness itself it always makes a true 
affirmation, and always does this in the same way. Hence, if the judgment of a sense is true, 
as these men claimed, it also follows that the nature of sweetness is necessarily such as it is; 
and thus something will be definitely true in reality. And it also follows that both an 
affirmation and a negation can never be true at the same time, because a sense never affirms 
that something is both sweet and not sweet at the same time, as has been stated. 

704. Yet all these (374). 

He gives the sixth argument. He says that, just as all of the above-mentioned theories or 
opinions destroy substantial predicates, as has been shown above (341 :C 625), in a similar 
way they destroy all necessary predicates. For it follows that nothing could ever be predicated 
of anything else either substantially or necessarily. That nothing could be predicated of 
anything else substantially is clear from what has been stated above. That nothing could be 
predicated of anything else necessarily is proved as follows. That is necessary which cannot 
be otherwise than it is; therefore, if everything which is can exist in one way or in another 
way, as is held by those who say that contradictories and opposite opinions are true at the 
same time, it follows that nothing is necessary in the world. 

705. And in general (375). 

Then he gives the seventh argument. He says that, if everything which appears is true, and a 
thing is true only insofar as it appears to the senses, it follows that a thing exists only insofar 
as, it is actually being sensed. But if something exists only in this way, i.e., insofar as it is 
being sensed, then it follows that nothing would exist if the senses did not exist; and this 
would follow if there were no animals or living things. But this is impossible. 


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706. For this can be true, that sensibles under the aspect of their sensibility do not exist; i.e., if 
they are considered under the aspect of sensibles actualized, they do not exist apart from the 
senses, for they are sensibles actualized insofar as they are present in a sense. And according 
to this every actualized sensible is a certain modification of the subject sensing, although this 
would be impossible if there were no sensory beings. But that the sensible objects which 
cause this modification in a sense should not exist is impossible. This becomes clear as 
follows: when some subsequent thing is removed it does not follow that a prior thing is 
removed. But the thing producing the modification in a sense is not the perception itself, 
because a perception is not the perception of itself but of something else, and this must be 
naturally prior to the perception just as a mover is prior to the thing which is moved. For sight 
does not see itself but sees color. 

707. And even if someone were to raise the objection that a sensible object and a sense are 
correlative and thus naturally simultaneous, so that when one is destroyed the other is 
destroyed, Aristotle's thesis is still true; for what is potentially sensible is not said to be 
relative to a sense because it is referred to a sense, but because the sense is referred to it, as is 
stated in Book V of this work (496:C 1027)- It is dearly impossible, then, to say that some 
things are true because they appear to the senses; yet this is what those men maintain who 
claim that all appearances are true, as is evident from the foregoing statements. 


LESSON 15 

Refutation of the View that Contradictories Can Be Shown to Be True at the Same Time. 
Contraries Cannot Belong to the Same Subject at the Same Time 

ARISTOTLE'S TEXT Chapter 6: 1011a 3-101 lb 22 

376. Now there are some, both of those who have been convinced by theories of this kind and 
of those who merely state them, who raise a difficulty; for they ask who it is that judges a 
man to be healthy, and in general who it is that judges rightly in each particular case. But such 
difficulties are like wondering whether we are now asleep or awake; and all such difficulties 
amount to the same thing. For these people think it fitting that there should be a reason for 
everything; for they are seeking a starting point, and they think they can get this by 
demonstration. Yet that sometimes they are not convinced they make evident in their actions. 
But according to what we have said this is characteristic of them; for they are seeking a 
reason for things for which no reason can be given, because the starting point of 
demonstration is not demonstration. These men, then, might easily believe this truth, for it is 
not difficult to grasp. 

377. But those who seek compulsion only in words are seeking the impossible. For they deem 
it right to speak as they do, and immediately say contrary things. 

378. Yet if not all things are relative but some things are absolute, not everything which 
appears will be true; for that which appears appears to someone. Thus he who says that all 
things which appear are true, makes all things which are, relative. Hence, those who look for 
compulsion in words, and think it fitting to maintain this view at the same time, must be 
careful to add that it is not what appears that is true, but what appears for him to whom it 
appears, and at the time when it appears, and in the manner in which it appears, and so on. 


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And if they maintain their view but not in this way, it will soon happen that they are saying 
contrary things. For it is possible that the same thing may appear to be honey to the sense of 
sight but not to the sense of taste, and that, since we have two eyes, things will not appear the 
same to each if their sight is unequal. Now, as we have stated, there are some who say, for the 
reasons already given (357), that what appears is true, and that all things are therefore equally 
true and false, because they do not always appear the same to all men or to the same man (for 
they do not always happen to be the same) but often have contrary appearances at the same 
time. For touch says there are two objects when the fingers are crossed, but sight says there is 
one. And in answering these men we must say that what appears is true, but not for the same 
man and in the same way and at the same time, so that when these qualifications are added 
what appears will be true. But perhaps it is for this reason that those who argue thus, not 
because of some difficulty but for the sake of argument, must say that this is not true but true 
for this person. 

379. And, as has been said before (378), they must make everything relative both to opinion 
and to perception, so that nothing has come to be or will come to be unless someone has first 
formed an opinion about it. But if something has come to be or will come to be, it is evident 
that not all things depend on opinion. 

380. Further, if a thing is one, it is relative to one thing or to a determinate number; and if the 
same thing is both half and equal, still the equal is not relative to the double or the half to the 
equal. If, then, in relation to the thinking subject, man and the object of thought are the same, 
man will not be the thinking subject but the object of thought. And if each thing is relative to 
the thinking subject, the thinking subject will be relative to things infinite in species. 

381. Let this suffice, then, regarding the points under discussion: that the firmest opinion of 
all is the one which asserts that opposite statements are not true at the same time; the 
conclusions that follow for those who say that they are true; and why they speak as they do. 

382. But since it is impossible for contradictories to be true of the same subject at the same 
time, it is evident that contraries cannot belong to the same subject at the same time; for one 
of two contraries is a privation. But a privation is nothing less than the negation of substance 
from some determinate genus. Therefore, if it is impossible to affirm and deny something 
truly at the same time, it is also impossible for contraries to belong to the same subject at the 
same time; but either both belong in a certain respect, or the one in a certain respect and the 
other absolutely. 

COMMENTARY 

708. He argues against those who adopted the above-mentioned theory not because of any 
reason but merely because they are obstinate; and in regard to this he does two things. First 
(376:C 7o8), he shows how these men were moved to adopt this opinion; and second (377:C 
71 1), how thit opinion must be dealt with ("But those who"). 

He accordingly says, first (376), that, besides the foregoing thinkers who adopted the 
above-mentioned opinion because of certain difficulties, there are some "among those who 
have been persuaded to accept these views," or opinions (i.e., those who continue to deceive 
themselves and have only these arguments to support their view), who raise a question. 
Another translation reads: "Now there are some, both of those who have been convinced by 
theories of this kind and of those who merely state them, who are puzzled or raise a 
question." And this statement means that some of those who are puzzled, i.e., some of those 


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who hold the above-mentioned opinion, consider only these difficulties and use the arguments 
which are given below. For if someone says to them that in the case of contrary opinions we 
should believe those persons who are healthy rather than those who are ill, and those who are 
wise rather than those who are ignorant, and those who are awake rather than those who are 
asleep, they will immediately ask how it is possible to distinguish with certainty between a 
healthy person and a sick one, and one who is awake and one who is asleep, and one who is 
wise and one who is foolish. In short, regarding all differences of opinion they will ask how it 
is possible to decide which one of these judges rightly in each particular case; for a man may 
seem to be wise to some and foolish to others, and the same applies in other cases. 

709. But these questions are foolish, for they are similar to the question whether we are now 
asleep or awake; for the distinction between all of these is not essential. Yet all of the 
foregoing difficulties amount to the same thing since they have a common root. For these 
sophists desire that demonstrative arguments should be given for all things; for it is obvious 
that they wanted to take some starting point which would be for them a kind of rule whereby 
they could distinguish between those who are healthy and those who are ill, and between 
those who are awake and those who are asleep. And they were not content to know this rule 
in just any way at all but wanted to acquire it by demonstration. That these men were in error, 
then, becomes evident from their actions, according to what has been said. And from these 
considerations it appears that their position is false; for if the judgments of one who is asleep 
and of one who is awake were equally good, then the same thing would result from each 
judgment when men act. But this is clearly false. Another text says, "But that sometimes they 
are not convinced they make evident in their actions"; and this statement is the clearer one in 
the light of the things laid down above. For although these men maintain this view and raise 
such questions, still they are not deceived in their own mind so that they believe the judgment 
of one who is asleep and the judgment of one who is awake to be equally true. And this is 
clear from their actions, as has been pointed out. 

710. But even though they are not deceived so as to be perplexed in this matter, this 
"nevertheless is characteristic of them," i.e., this weakness of mind that they should seek a 
demonstrative argument for things for which no demonstration can be given. For "the starting 
point of demonstration is not demonstration"; i.e., there can be no demonstration of it. And 
this is easy for them to believe, because this too is not difficult to grasp by demonstration; for 
a demonstrative argument proves that not all things can be demonstrated, otherwise there 
would be an infinite regress. 

711. But those who (377). 

He now argues against the other philosophers, i.e., against those who were not moved to 
maintain that all appearances are true on the grounds that no rule can be established 
demonstratively whereby it is possible to distinguish with certainty between those who judge 
rightly and those who do not, but who hold the above-mentioned theory or view only because 
they are insolent. 

In regard to this he does three things. First (377:C 71 1), he shows that such insolence tends to 
lead to an impossible conclusion. Second (378:C 712), he indicates the way in which it seems 
necessary to oppose them ("Yet if not all things"). Third (379:C V6), he explains how we 
must meet their argument from the viewpoint of truth ("And, as has been"). 

He accordingly says, first (377), that those who seek "compulsion merely in words," i.e., 
those who are not moved by any reason or because of the difficulty involved in some problem 


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or because of some failure in demonstration but depend solely on words and believe that they 
can say anything which cannot be disproved-such people as these want to argue to an 
impossible conclusion. For they want to adopt the principle that contraries are true at the same 
time on the grounds that all appearances are true. 

712. Yet if not all (378). 

Then he shows how we may oppose these men by using their own position and avoid the 
foregoing impossible conclusion. He says that, unless everything which is, is claimed to be 
relative, it cannot be said that every appearance is true. For if there are some things in the 
world which have absolute being and are not relative to perception or to opinion, being and 
appearing will not be the same; for appearing implies a relation to perception or to opinion, 
because that which appears appears to someone; and thus whatever is not an appearance must 
be true. It is clear, then, that whoever says that all appearances are true, makes all beings 
relative, i.e., to perception or to opinion. Hence, in opposing the foregoing sophists who seek 
compulsion in words, we may say that, if anyone thinks it fitting "to grant this view," i.e., to 
concede this opinion which they maintain, he must be careful, or observant, lest he be led to 
admit that contradictories are true at the same time; for it should not be said unqualifiedly that 
everything which appears is true, but that what appears is true for the one to whom it appears, 
and inasmuch as it appears, and when it appears, and in the manner in which it appears. We 
would be allowed to add these qualifications on the grounds that a thing does not have being 
in an absolute sense but only relatively. 

713. Now this should be noted by those who want to adopt this position, because if someone 
were to grant them that every appearance is true, and thus not admit the above-mentioned 
qualifications, as has been stated, it would follow immediately that he is saying that contraries 
are true at the same time. For it is possible that the same thing may appear to be honey to the 
sense of sight because its color resembles that of honey, and not appear to be honey to the 
sense of taste because it does not taste like honey. And similarly when two eyes are unlike, 
the vision which is had through each is not the same, or the visual impressions which we get 
through each eye do not seem the same. For example, if the pupil of one eye were infected by 
some gross or dark vapor, and the other were free of this, all things would seem dark or 
obscure through the infected eye but not through the good one. I say, then, that one must be 
careful, or observant, because this is necessary in confronting the foregoing sophists, who 
say, for the reasons given above (376:C 708), that every appearance is true. 

714. And from this position it would also follow that all things are equally true and false, 
because they do not appear the same to all men or even the same to one man, since the same 
man very often makes contrary judgments about the same thing at the same time on the basis 
of different senses; for example, sight judges that thing to be one which touch judges to be 
two, because when the fingers are crossed it happens that the same tangible object is sensed 
by different organs of touch; that is, the contact through different fingers affects the tactual 
power as though there were two tangible objects. But it does not seem to the same man 
through the same sense and in the same way and at the same time that this is true namely, that 
contraries are true at the same time. 

715. Therefore, it is perhaps necessary to use this answer against the above-mentioned 
sophists who argue thus not because of some difficulty but for the sake of argument (as 
though upholding this statement for its own sake because they are perverse), namely, that this 
is not true absolutely but true for this person. For it does not follow from this that 
contradictories are true at the same time, because it is not contradictory that something should 


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be true for one person and not true for another. 

716. And, as has been said (379). 

He tells us that we should oppose the foregoing sophists from the standpoint of the truth and 
not just offer an argument ad hominem, namely, not by granting the false opinion which they 
maintain. And he does this by means of two arguments. The first is this: as has been stated 
before, if everything which appears is true, they must "make all things relative," i.e., to 
perception or to opinion. Now from this the untenable position follows that nothing may exist 
or come to be if it is not thought of in some way. But if this is false (because' many things are 
and come to be of which there is neither opinion nor knowledge, for example, things which 
exist in the depths of the sea or in the bowels of the earth), it is evident that not all things are 
relative, i.e., to perception or to opinion. Hence not every appearance is true. 

717. Further, if a thing (380). 

He gives the second argument. He says that what is one is relative only to one thing, and not 
to any one thing at all but to a determinate one. For example, it is clear that the half and the 
equal may be the same in their subject, yet the double is not said to be relative to the equal but 
rather to the half; but equal is said to be relative to equal. Similarly, if man himself as a 
thinking subject is also the object of thought, man is not relative to the thinking subject as a 
thinking subject, but as the object of thought. If, then, all beings are relative to a thinking sub 
iect as such, it follows that what I call the thinking subject is not one, since one is relative 
only to one, but it is an infinite number of things in species, since an infinite number of things 
are related to it. But this is impossible. Hence it cannot be said that all things are said to be 
relative to a thinking subject, or that everything which appears so, or is thought to be so, is 
therefore true. 

718. Let this suffice (381). 

He now draws his intended conclusion, and in regard to this he does two things. First, he 
draws his main conclusion; and second (382:C 719), he derives a corollary from it ("But since 
it is impossible"). 

He accordingly says, first (381), that it is clear from the above statement that the most certain 
of all opinions or views is the one which states that opposite statements or propositions, i.e., 
contradictory ones, are not true at the same time. And the impossible conclusions which face 
those who say that they are true at the same time, and the reason which moved them to say 
this, have also been explained. 

719. But since it is impossible (382). 

He draws the corollary. He says that, since it is impossible, from what has been said, for two 
contradictories to be true of the same subject at the same time, it is also evident that contraries 
cannot belong to the same subject; for the privative character of one of two contraries is no 
less evident in the case of contraries than it is in the case of other opposites, although each of 
two contraries is a positive reality; for it does not consist in affirmation and negation or in 
privation and possession. For one of them is imperfect when compared with the other, as 
black when compared with white, and bitter with sweet; and thus it has a kind of privation 
added to it. But privation is negation of substance, i.e., in some determinate subject. And it is 
also the deprivation of some determinate genus; for it is a negation within a genus. For not 


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everything which does not see is said to be blind, but only that which is found in the genus of 
seeing things. It is clear, then, that a contrary includes privation, and that privation is a kind of 
negation. Hence, if it is impossible both to affirm and to deny something at the same time, it 
is also impossible for contraries to belong absolutely to the same subject at the same time; but 
either "both belong to it," i.e., relatively, as when both are present potentially or partially, or 
one is present in a certain respect and the other absolutely; or one is present in many and the 
more important parts, and the other only in some part; for example, an Ethiopian is black 
absolutely and white as regards his teeth. 


LESSON 16 

No Intermediate between Contradictories. How Heraclitus and Anaxagoras Influenced This 
Position 

ARISTOTLE'S TEXT Chapter 7: 1011b 23-1012a 28 

383. Neither can there be an intermediate between contradictories, but of each subject it is 
necessary either to affirm or to deny one thing. This first becomes evident when people define 
what truth and falsity are; for to say that what is, is not, or that what is not, is, is false; and to 
say that what is, is, or that what is not, is not, is true. Hence he who affirms that something is 
or is not will say either what is true or what is false. But neither what is nor what is not is said 
to be or not to be. 

384. Further, an intermediate between contradictories will be such either in the way that green 
is an intermediate between white and black, or as what is neither a man nor a horse is an 
intermediate between a man and a horse. If it is of the latter sort, there will then be no change; 
for change is from what is good to what is not-good, or from the latter to the former. But that 
this now occurs is always apparent; for change takes place only between opposites and 
intermediates. But if it is a true intermediate, then in this case there will be a kind of change 
to something white, but not from what is not-white. However, this is not now apparent. 

385. Further, the mind either affirms or denies every sensible and intelligible object. This is 
clear from the definition, because it expresses what is true or what is false. Indeed, when the 
mind composes in this way by affirming or denying, it says what is true; and when it does it 
otherwise, it says what is false. 

386. Again, there must be an intermediate in addition to all contradictories, unless one is 
arguing for the sake of argument. In that case one will say what is neither true nor false. And 
then there will be something else besides being and non-being; and therefore there will also 
be some kind of change besides generation and corruption. 

387. Again, there will also be an intermediate in all those classes of things in which the 
negation of a term implies its contrary; for example, in the class of numbers there will be a 
number which is neither even nor odd. But this is impossible, as is evident from the 
definition. 

388. Further, there will be an infinite regress, and there will be things which are related not 
only as half again as much but even more. For it will also be possible to deny the intermediate 


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both with reference to its affirmation and to its negation; and this again will be something, for 
its substance is something different. 

389. Again, when one answers "no" to the question whether a thing is white, he has denied 
nothing except that it is; and its not-being is a negation. 

390. Now some men have formed this opinion in the same way that other unreasonable 
opinions have been formed; for when they cannot refute eristic arguments, they assent to the 
argument and claim that the conclusion is true. Some men hold this view, then, for this 
reason, and others because they seek an explanation for everything. 

391. The starting point to be used against all of these people is the definition, and the 
definition results from the necessity of their meaning something; for the concept, of which the 
word is a sign, is a definition. 

392. Now the statement of Heraclitus, which says that all things are and are not, seems to 
make all things true; and the statement of Anaxagoras that there is an intermediate between 
contradictories seems to make everything false; for when all things are mixed together, the 
mixture is neither good nor not good, so that it is impossible to say anything true. 

COMMENTARY 

720. Having argued dialectically against those who maintain that contradictories are true at 
the same time, Aristotle now argues against those who maintain that there is an intermediate 
between contradictories; for these thinkers do not always say that the one or the other part of 
a contradiction is true. In regard to this he does two things. First (383:C 720), he argues 
against this position. Second (393 :C 736), he argues against certain other unreasonable 
questions which follow from this position and from the one above ("With these points"). 

In regard to the first he does two things. First, he raises arguments against the position 
mentioned. Second (390:C 730, he gives the reason why some thinkers have been moved to 
hold this position ("Now some men"). 

In regard to the first part he gives seven arguments. He says, first (383), that, just as 
contradictories cannot be true at the same time, neither can there be an intermediate between 
contradictories, but it is necessary either to affirm or deny one or the other. 

721. This first becomes evident from the definition of truth and falsity; for to say what is false 
is simply to say that what is, is not, or that what is not, is. And to say what is true is simply to 
say that what is, is, or that what is not is not. It is clear, then, that whoever says that 
something is, says either what is true or what is false; and if he says what is true, it must be 
so, because to say what is true is to say that what is, is. And if he says what is false, it must 
not be so, because to say what is false is simply to say that what is, is not. The same thing 
applies if he says that something is not; for if he says what is false, it must be; and if he says 
what is true, it must not be. Therefore, either the affirmation or the negation is necessarily 
true. But he who holds that there is an intermediate between contradictories does not claim 
that it is necessary to say that what is either is or is not; nor does he claim that it is necessary 
to speak in this way about what is not. Thus neither he who affirms nor he who denies need 
say what is true or what is false. 

722. Further, an intermediate (384). 


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He gives the second argument, which runs thus: an intermediate between any two 
contradictories can be understood in one way as something that participates in each of the 
extremes, and this is an intermediate in the same genus, as green or yellow is an intermediate 
between white and black; or in another way as something that is the negation of each extreme, 
and such an intermediate is different in genus; for example, a stone, which is neither a man 
nor a horse, is an intermediate between a man and a horse. Therefore, if there is an 
intermediate between contradictories, it will be such either in the first way or in the second. 

723. If it is an intermediate in the second way, there will be no change. This becomes clear as 
follows: every change is from what is not- good to what is good, or from what is good to what 
is not-good. Hence, since change is between contraries, for example, white and black, change 
must take place between things which are opposed as contradictories; for black is not white, 
as is clear from the above statements. But according to the foregoing position there cannot be 
change from what is not-good to what is good, or the reverse. Hence there will be no change. 
Yet it always appears or seems that change proceeds from what is not-good to what is good, 
or the reverse. That every change of this sort would be destroyed if the foregoing position is 
true 'becomes clear as follows. Change can take place only between contraries and 
intermediates which belong to the same genus. But there can be a change from one extreme to 
another only through an intermediate. Therefore, if there is an intermediate between 
contradictories as the negation of both, i.e., as something belonging to a different genus, it 
will be impossible for change to take place between an extreme and an intermediate, and 
therefore between one extreme and another. 

724. And if it is an intermediate in the first way, so that the intermediate between 
contradictories belongs to the same genus by participating in both, as yellow is an 
intermediate between white and black, 'this impossible conclusion follows: there will be 
some process of generation which terminates in white and does not come from the not-white, 
because change proceeds not only from one extreme to another but also from an intermediate. 
But it does not seem to be true that there is any process of change terminating in the white 
which does not proceed from the not- white. Thus it is clear that there is no way at all in which 
there can be an intermediate between contradictories. 

725. Further, the mind (385). 

He gives the third argument, which runs thus: in every one of the conceptions by which the 
intellect knows or understands, it either affirms or denies something. Now from the definition 
of truth and falsity it seems that whether one affirms or denies he must say what is true or 
what is false; because when the intellect composes in this way, either by affirming or denying 
as the matter stands in reality, it expresses what is true; but when it does it otherwise, it 
expresses what is false. Thus it is clear that a true statement must always be either an 
affirmation or a negation, because some opinion must be true, and every opinion is either an 
affirmation or a negation. Hence it must always be either an affirmation or a negation that is 
true; and thus there is no intermediate between contradictories. 

726. Again, there must (386). 

Then he gives the fourth argument, which runs thus: if one maintains that there must be an 
intermediate between contradictories, then it is necessary to say that in the case of all 
contradictories there must be besides the contradictories themselves something true which is 
an intermediate between them, unless this person is arguing "for the sake of argument," i.e., 
without any real reason but only because it pleases him to speak in this way. But this cannot 


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be true in all cases, because the true and the not-true are contradictories. Thus it would follow 
that there is someone who says what is neither true nor false. But the opposite of this was 
made clear from the definition of truth and falsity. 

727. Similarly, since being and nonbeing are contradictories, it will follow that there is 
something besides being and non-being, and thus there will be some kind of change besides 
generation and corruption; for generation is a change to being, and corruption a change to 
non-being. Therefore there can be no intermediate between contradictories. 

728. Again, there will (387). 

He gives the fifth argument. He says that in some genera a negation takes the place of a 
contrary difference; or, according to another text, "negation supplies the contrary," because 
one of two contraries, which must be in the same genus, derives its definition from negation, 
as is clear in the case of the even and the odd, and the just and unjust. Therefore, if there is an 
intermediate between affirmation and negation, there will be some intermediate between all 
these contraries, since they obviously depend on affirmation and negation; for example, in the 
case of number, there will be some number which is neither even nor odd. But this is clearly 
impossible in the light of the definition of the even and the odd; for the even is what can be 
divided into equal numbers, and the odd is what cannot. Therefore it follows that there cannot 
be an intermediate between affirmation and negation. 

729. Further, there will (388). 

He now gives the sixth argument: those who claim that there is an interinediate between an 
affirmation and a negation hold some third thing besides these two, which all posit in 
common, saying that there is nothing intermediMe between them. But three is related it) two 
"as half again as much," i.e., in a proportion of one and a half to one. Therefore, according to 
the opinion of 

those who hold an intermediate between an affirmation and a negation it appears at first sight 
that all things "will be related as half again as much," i.e., in a proportion of one and a half to 
one to the things which are given, because there will be not only affirmations and negations 
but also intermediates. And this is not the only conclusion that follows, but it also follows that 
there will be many more things in infinite regression. For it is evident that everything which 
can be affirmed can also be denied. But if it is possible to affirm that the following three 
things exist: an affirmation, a negation and an intermediate, it is then also possible to deny 
these three. And just as a negation differs from an affirmation, in a similar way there will also 
be some fourth thing which differs from the three mentioned; for it will have a different 
substance and intelligible structure than those just mentioned, in the same way that a negation 
has a different substance and intelligible structure from an affirmation. And it is possible to 
deny these four, and the negations of these will be true; and so on to infinity. Hence there will 
be infinitely more things than have just been posited. This seems absurd. 

730. Again, when one (389). 

He gives the seventh argument, and it runs as follows: if someone were to ask whether a man 
or some other thing is white, the one answering him must say either "yes" or "no." If he says 
"yes," it is plain that he says that the affirmation is true; but if he does not affirm this but says 
"no," it is clear that he denies this. Now the only thing which he denies is what he was asked, 
and the negation of this is non-being because it is negative. Therefore it follows that, when he 


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answers this question, he must of necessity either admit the affirmative or assert the negative. 
Hence there is no intermediate between these two. 

731. Now some men (390). 

He gives the reason why some men adopt this opinion, and in regard to this he does three 
things. First, he shows why some men have held this opinion. Second (391 :C 733), he 
explains how one can argue dialectically against them ("The starting point"). Third (392:C 
734), he notes the philosophical views on which the foregoing opinions depend ("Now the 
statement") 

He accordingly says, first (390), that the foregoing opinion, like other unreasonable opinions, 
is adopted by certain thinkers for one of two reasons. The first is this: when some men cannot 
refute "eristic arguments," i.e., disputatious or sophistical arguments, which are presented to 
them either by others or by themselves, they agree with the one giving the argument and 
assent to the conclusion, saying that what has been shown is true. And then they try to 
confirm this by devising other arguments. 

732. The second reason why men adopt this position is that some men want to discover an 
argument to prove everything, and therefore whatever cannot be proved they do not want to 
affirm but deny. But first principles, which are the common conceptions of all men, cannot be 
proved. Hence these men deny them and thereby adopt unreasonable views. 

733. The starting point (391). 

He indicates the starting point from which one must proceed to argue against such opinions. 
He says that the starting point is derived from the definitions of truth and falsity, or from the 
definitions of other terms, as is clear from the arguments given above. For men must admit 
the definitions of things if they hold that words signify something; for the intelligible 
expression of a thing which a word signifies is a thing's definition. But if they do not admit 
that all words signify something, they do not differ from plants, as has been said above 
(348:C652). 

734. Now the statement (392). 

Here he gives the opinion on which the foregoing opinions depend. He says that these 
opinions stem from the position of Heraclitus, who said that all things are in motion, and 
therefore that they both are and are not at the same time. And since what is being moved has 
non-being mixed with being, it follows that everything is true. 

735. And from the position of Anaxagoras it follows that there is an intermediate between 
contradictories; for he held that everything is mixed with everything, because everything 
comes from everything. But neither of the extremes can be predicated of the mixture; for 
example, intermediate colors are neither whiteness or blackness. Hence the mixture is neither 
good nor not-good, neither white nor not-white; and thus there is an intermediate between 
contradictories. It follows, then, that everything is false; for according to the common opinion 
we posit nothing but affirmation and negation. Hence, if both an affirmation and its negation 
are false, it follows that everything is false. 


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LESSON 17 

Rejection of the opinions that Everything Is True and False, and that Everything Is at Rest 
and in Motion 

ARISTOTLE'S TEXT Chapter 8: 1012a 29-1012b 31 

393. With these points settled it is evident that the theories which have been expressed 
univocally and about all things cannot be true as some affirm them to be. Now some say that 
nothing is true (for they say that there is nothing to prevent all statements from being like the 
statement that the diagnoal of a square is commensurable with one of its sides), and others say 
that everything is true. These views are almost the same as that of Heraclitus; for he who says 
that all things are true and all false admits both views apart from his own words. Hence, if 
those are impossible, these also must be impossible. 

394. Further, it is evident that there are contradictories which cannot be true at the same time. 
Nor can they all be false, though this would seem more possible from what has been said. 

395. But in opposing all such views it is necessary to postulate, as has been stated in the 
above discussion (332), not ' that something is or is not, but that a word signifies something. 
Hence it is necessary to argue from a definition, once we have accepted what truth and falsity 
mean. But if to say what is true is merely to deny what is false, not everything can be false. 
For one part of a contradiction must be true. 

396. Again, if everything must be either affirmed or denied, both cannot be false; for one part 
of a contradiction is false. 

397. And the view commonly expressed applies to all such theories — they destroy 
themselves; for he who says that everything is true makes the contrary of his own statement 
true, and thus makes his own not true; for the contrary denies that it is true. And he who says 
that everything is false makes his own statement false. But if the former makes an exception 
of the contrary statement, saying that it alone is not true, and the latter makes an exception of 
his own statement, saying that it is not false, still they will have to consider the truth and 
falsity of an infinite number of statements. For he who says that a true statement is true is 
right; and this process will go on to infinity. 

398. Now it is evident that those who say that all things are at rest do not speak the truth, and 
neither do those who say that all things are in motion. 

399. For if all things are at rest, the same thing will always be true and false; btit this seems to 
be something that changes, for he who makes a statement at mic time was not and again will 
not be. 

400. And if all things are in motion, nothing will be true, and so everything will be false. But 
it has been shown that this is impossible. 

401. Further, it must be some being which is changed; for change is from something to 
something. 

402. But it is not true that all things are at rest or in motion sometimes, and nothing always; 
for there is something which always moves the things that are being moved, and the first 


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mover is itself immovable. 

COMMENTARY 

736. He argues dialectically against certain positions which stem from those mentioned 
above. First (393:C736), he argues against certain men who destroy the principles of logic; 
and second (398:C 744), against certain men who destroy the principles of natural philosophy 
("Now it is evident"). 

For first philosophy should argue dialectically against those who deny the principles of the 
particular sciences, because all principles are based on the principle that an affirmation and a 
negation are not true at the same time, and that there is no intermediate between them. Now 
these principles are the most specific principles of this science, since they depend on the 
concept of being, which is the primary subject of this branch of philosophy. But the true and 
the false belong specifically to the study of logic; for they depend on the kind of being which 
is found in the mind, with which logic deals; for truth and falsity exist in the mind, as is stated 
in Book VI of this work (558:C 1231). Motion and rest, on the other hand, belong properly to 
the study of natural philosophy, because nature is defined as a principle of motion and of rest. 
Now the error made about truth and falsity is a result of the error made about being and 
nonbeing, for truth and falsity are defined by means of being and non-being, as has been said 
above. For there is 'truth when one says that what is, is, or that what is not, is not; and falsity 
is defined in the opposite way. And similarly the error made about rest and motion is a result 
of the error made about being and non-being; for what is in motion as such does not yet exist, 
whereas what is at rest already is. Hence, when the errors made about being and non-being 
have been removed, the errors made about truth and falsity and rest and motion will then also 
be removed. 

737. Regarding the first part of this division he does two things. First (393:C 737), he gives 
the erroneous opinions about truth and falsity. Second (394:C 739), he criticizes these 
opinions ("Further, it is evident"). 

Thus he says (393) that, "with these points settled," i.e., with the foregoing points established 
which have to be used against the paradoxical positions mentioned above, it is obviously 
impossible that the views of some men should be true, namely, that we must form an opinion 
"univocally," i.e., think in the same way, about all things, so that we should say that all things 
are equally true or equally false. For some thinkers said that nothing is true but everything 
false, and that there is nothing to prevent us from saying that all statements are just as false as 
the statement (which is false) that the diameter of a square is commensurate with one of its 
sides. But others have said that all things are true. Statements of the latter kind are a result of 
the opinion of Heraclitus, as has been pointed out (362:C 684); for he said that a thing is and 
is not at the same time, and from this it follows that everything is true. 

738. And lest perhaps someone might say that besides these opinions there is also a third one, 
which states that everything is both true and false at the same time, he replies, as though 
meeting a tacit objection, that anyone who maintains this opinion also maintains both of the 
foregoing ones. Hence, if the first two opinions are impossible, the third must also be 
impossible. 

739. Further, it is evident (394). 


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Then he presents arguments against the foregoing opinions, and the first of these is as 
follows: it is evident that there are certain contradictories which cannot be true at the same 
time or false at the same time, for example, the true and not-true, being and non-being. This 
can be better understood from what has been said. Therefore, if one of these two 
contradictories must be false and the other true, not all things can be true or all false. 

740. But in opposing (395). 

He gives the second argument. He says that in opposing "these views," or positions, "it is 
necessary to postulate," or request, not that someone should admit that something either is or 
is not in reality, as has been stated above (332:C 611), because this seems to be begging the 
question, but that he should admit that a word signifies something. Now if this is not granted, 
the dispute comes to an end; but if it is granted, it is then necessary to give definitions, as has 
already been stated above (332:C 611). Hence we must argue against these thinkers by 
proceeding from definitions, and in the case of the present thesis we must do this especially 
by considering the definition of falsity. Now if truth consists merely in affirming what it is 
false to deny, and vice versa, it follows that not all statements can be false, because either the 
affirmation or the negation of something must be true. For obviously truth consists simply in 
saying that what is, is, or in saying that what is not, is not; and falsity consists in saying that 
what is, is not, or in saying that what is not, is. Hence it is clear that it is true to say that that is 
of which it is false that it is not, or to say that that is not of which it is false that it is; and it is 
false to say that that is of which it is true that it is not, or to say that that is not of which it is 
true that it is. Thus from the definition of truth and falsity it is clear that not all things are 
false. And for the same reason it is clear that not all things are true. 

741. Again, if everything (396). 

Here he gives the third argument, which runs thus: it is clear from what has been said above 
that we must either affirm or deny something of each thing since there is no intermediate 
between contradictories. It is impossible, then, for everything to be false. And by the same 
reasoning it is proved that it is impossible for everything to be true, i.e., by reason of the fact 
that it is impossible both to affirm and to deny something at the same time. 

742. And the view (397). 

He gives the fourth argument: all of the foregoing statements, or opinions, face this 
unreasonable result-they destroy themselves. This is "the view commonly expressed," i.e., a 
frequently heard statement made by all; and thus another text says, "It happens that it is 
commonly held." He proves this view as follows: anyone who says that everything is true 
makes the contrary of his own opinion true. But the contrary of his own opinion is that his 
own opinion is not true. Therefore he who says that everything is true says that his own 
opinion is not true; and thus he destroys his own opinion. Similarly it is evident that he who 
says that everything is false also says that his own opinion is false. 

743. And because someone could say that he who claims that everything is true makes an 
exception of the one contrary to his own statement or bars it from what holds universally (and 
the same thing applies to one who says that everything is false), he therefore 

rejects this answer. He says that, if the one who says that everything is true makes his own 
contrary opinion an exception, saying that it alone is not true, and if the one who says that 
everything is false makes his own opinion an exception, saying that it alone is not false, none 


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the less it follows that they will be able "to consider," or bring forward, an infinite number of 
true statements against those who hold that all are false, and an infinite number of false 
statements against those who hold that all are true. For granted that one opinion is true, it 
follows that an infinite number are true. And granted that one opinion is false, it follows that 
an infinite number are false. For if the position, or opinion, that Socrates is sitting is true, then 
the opinion that it is true that Socrates is sitting will also be true, and so on to infinity. For he 
who says that a true statement is true is always right; and he who says that a false statement is 
true is always wrong; and this can proceed to infinity. 

744. Now it is (398). 

He argues against those who destroy the principles of nature, i.e., motion and rest, and in 
regard to this he does three things. 

First, he mentions the falsity of these opinions, saying that it is evident, from what has been 
said above, that neither the opinion which states that everything is in motion, nor the one 
which states that everything is at rest, is true. 

745. For if all things (399). 

Second, he shows that these opinions are false. First of all he shows that the opinion which 
holds that everything is at rest is false; for if everything were at rest, 'nothing would then be 
changed from the state in which it sometimes is. Hence, whatever is true would always be 
true, and whatever is false would always be false. But this seems to be absurd; for the truth 
and falsity of a proposition is changeable. Nor is this to be wondered at, because the man who 
has an opinion or makes a statement at one time was not and now is and again will not be. 

746. Second, he uses two arguments to show that the opinion which holds that all things are 
in motion is false. He gives the first (400) where he says, "And if all things." It is as follows. 
If all things are in motion and nothing is at rest, nothing will be true in the world; for what is 
true already exists, but what is in motion does not yet exist. Hence everything must be false. 
But this is impossible, as has been shown (395:C 740). 

747. Further, it must be (401). 

He gives the second argument, and it runs thus: everything that is undergoing change is 
necessarily a being, because everything that is being changed is being changed from 
something to something else, and everything that is being changed in something else belongs 
to the subject that is undergoing change. Hence it is not necessary to say that everything in the 
subject undergoing change is being changed, but that there is something which remains. 
Hence not everything is in motion. 

748. But it is not (402). 

He gives the third argument, and it disposes of a false opinion which could arise from what 
has been said above. For, since not all things are in motion nor all at rest, someone could 
therefore think that all things are sometimes in motion and sometimes at rest. In disposing of 
this opinion he says that, it is not true that all things are sometimes in motion and sometimes 
at rest, for there are certain movable things which are always being moved, namely, the 
celestial bodies above us, and there is a mover, namely, the first, which is always immovable 
and ever in the same state, as has been proved in Book VIII of the Physics. 


THE SUBJECT OF METAPHYSICS, DEMONSTRATIVELY 


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METAPHYSICS 
BOOK V 

DEFINITIONS 


CONTENTS 


LESSON 1: 
LESSON 2 
LESSON 3 
LESSON 4 
LESSON 5 
LESSON 6 
LESSON 7 

LESSON 8 

LESSON 9 

LESSON 10 
LESSON 11 
LESSON 12 
LESSON 13 

LESSON 14 

LESSON 15 

LESSON 16 
LESSON 17 
LESSON 18 

LESSON 19 

LESSON 20 

LESSON 21 
LESSON 22 


Five Senses of the Term "Principle." The Common Definition of Principle 

The Four Classes of Causes. Several Causes of the Same Effect. Causes May 
Be Causes of Each Other. Contraries Have the Same Cause 

All Causes Reduced to Four Classes 

The Proper Meaning of Element; Elements in Words, Natural Bodies, and 
Demonstrations. Transferred Usages of "Element" and Their Common Basis 

Five Senses of the Term Nature 

Four Senses of the Term Necessary. Its First and Proper Sense. Immobile 
Things, though Necessary, Are Exempted from Force 

The Kinds of Accidental Unity and of Essential Unity 

The Primary Sense of One. One in the Sense of Complete. One as the 
Principle of Number. The Ways in Which Things Are One. The Ways in 
Which Things Are Many 

Division of Being into Accidental and Essential. The Types of Accidental 
and of Essential Being 

Meanings of Substance 

The Ways in Which Things Are the Same Essentially and Accidentally 

Various Senses of Diverse, Different, Like, Contrary, and Diverse in Species 

The Ways in Which Things Are Prior and Subsequent 

Various Senses of the Terms Potency, Capable, Incapable, Possible and 
Impossible 

The Meaning of Quantity. Its Kinds. The Essentially and Accidentally 
Quantitative 

The Senses of Quality 

The Senses of Relative 

The Senses of Perfect 

The Senses of Limit, of "According to Which," of "In Itself," and of 
Disposition 

The Meanings of Disposition, of Having, of Affection, of Privation, and of 
"To Have" 

The Meanings of "To Come from Something," Part, Whole, and Mutilated 
The Meanings of Genus, of Falsity, and of Accident 


LESSON I 


METAPHYSICSBOOK V 


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Five Senses of the Term "Principle." The Common Definition of Principle 

ARISTOTLE'S TEXT Chapter 1: 1012b 34-1013a 23 

403. In one sense the term principle [beginning or starting point] means that from which 
someone first moves something; for example, in the case of a line or a journey, if the motion 
is from here, this is the principle, but if the motion is in the opposite direction, this is 
something different. In another sense principle means that from which a thing best comes into 
being, as the starting point of instruction; for sometimes it is not from what is first or from the 
starting point of the thing that one must begin, but from that from which one learns most 
readily. Again, principle means that first inherent thing from which something is brought into 
being, as the keel of a ship and the foundation of a house, and as some suppose the heart to be 
the principle in animals, and others the brain, and others anything else of the sort. In another 
sense it means that non-inherent first thing from which something comes into being; and that 
from which motion and change naturally first begins, as a child comes from its father and 
mother, and a fight from abusive language. In another sense principle means that according to 
whose will movable things are moved and changeable things are changed; in states, for 
example, princely, magistral, imperial, or tyrannical power are all principles. And so also are 
the arts, especially the architectonic arts, called principles. And that from which a thing can 
first be known is also called a principle of that thing, as the postulates of demonstrations. And 
causes are also spoken of in the same number of senses, for all causes are principles. 

404. Therefore, it is common to all principles to be the first thing from which a thing either is, 
comes to be, or is known. And of these some are intrinsic and others extrinsic. And for this 
reason nature is a principle, and so also is an element, and mind, purpose, substance, and the 
final cause; for good and evil are the principles both of the knowledge and motion of many 
things. 

COMMENTARY 
Principle 

751. Now it should be noted that, although a principle and a cause are the same in subject, 
they nevertheless differ in meaning; for the term principle implies an order or sequence, 
whereas the term cause implies some influence on the being of the thing caused. Now an 
order of priority and posteriority is found in different things; but according to what is first 
known by us order is found in local motion, because that kind of motion is more evident to 
the senses. Further, order is found in three classes of things, one of which is naturally 
associated with the other, i.e., continuous quantity, motion and time. For insofar as there is 
priority and posteriority in continuous quantity, there is priority and posteriority in motion; 
and insofar as there is priority and posteriority in motion, there is priority and posteriority in 
time, as is stated in Book IV of the Physics. Therefore, because a principle is said to be what 
is first in any order, and the order which is considered according to priority and posteriority in 
continuous quantity is first known by us (and things are named by us insofar as they are 
known to us), for this reason the term principle, properly considered, designates what is first 
in a continuous quantity over which motion passes. Hence he says that a principle is said to be 
"that from which someone first moves something," i.e., any part of a continuous quantity 
from which local motion begins. Or, according to another reading, "Some part of a thing from 
which motion will first begin"; i.e., some part of a thing from which it first begins to be 
moved; for example in the case of a line and in that of any kind of journey the principle is the 
point from which motion begins. But the opposite or contrary point is "something different or 


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other," i.e., the end or terminus. It should also be noted that a principle of motion and a 
principle of time belong to this class for the reason just given. 

752. But because motion does not always begin from the starting point of a continuous 
quantity but from that part from which the motion of each thing begins most readily, he 
therefore gives a second meaning of principle, saying that we speak of a principle of motion 
in another way "as that from which a thing best comes into being," i.e., the point from which 
each thing begins to be moved most easily. He makes this clear by an example; for in the 
disciplines one does not always begin to learn from something that is a beginning in an 
absolute sense and by nature, but from that from which one "is able to learn" most readily, 
i.e., from those things which are better known to us, even though they are sometimes more 
remote by their nature. 

753. Now this sense of principle differs from the first. For in the first sense a principle of 
motion gets its name from the starting point of a continuous quantity, whereas here the 
principle of continuous quantity gets its name from the starting point of motion. Hence in the 
case of those motions which are over circular continuous quantities and have no starting 
point, the principle is also considered to be the point from which the movable body is best or 
most fittingly moved according to its nature. For example, in the case of the first thing moved 
[the first sphere] the starting point is in the east. The same thing is true in the case of our own 
movements; for a man does not always start to move from the beginning of a road but 
sometimes from the middle or from any terminus at all from which it is convenient for him to 
start moving. 

754. Now from the order considered in local motion we come to know the order in other 
motions. And for this reason we have the senses of principle based upon the principle of 
generation or coming to be of things. But this is taken in two ways; for it is either "inherent," 
i.e., intrinsic, or "non-inherent," i.e., extrinsic. 

755. In the first way, then, a principle means that part of a thing which is first generated and 
from which the generation of the thing begins; for example, in the case of a ship the first thing 
to come into being is the base or keel, which is in a certain sense the foundation on which the 
whole superstructure of the ship is raised. And, similarly, in the case of a house the first thing 
that comes into being is the foundation. And in the case of an animal the first thing that comes 
into being, according to some, is the heart, and according to others, the brain or some such 
member of the body. For an animal is distinguished from a non-animal by reason of sensation 
and motion. Now the principle of motion appears to be in the heart, and sensory operations 
are most evident in the brain. Hence those who considered an animal from the viewpoint of 
motion held that the heart is the principle in the generation of an animal. But those who 
considered an animal only from the viewpoint of the senses held that the brain is this 
principle; yet the first principle of sensation is also in the heart even though the operations of 
the senses are completed in the brain. And those who considered an animal from the 
viewpoint of operation, or according to some of its activities, held that the organ which is 
naturally disposed for that operation, as the liver or some other such part is the first part 
which is generated in an animal. But according to the view of the Philosopher the first part is 
the heart because all of the soul' s powers are diffused throughout the body by means of the 
heart. 

756. In the second way, a principle means that from which a thing's process of generation 
begins but which is outside the thing. This is made clear in the case of three classes of things. 
The first is that of natural beings, in which the principle of generation is said to be the first 


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thing from which motion naturally begins in those things which come about through motion 
(as those which come about through alteration or through some similar kind of motion; for 
example, a man is said to become large or white); or that from which a complete change 
begins (as in the case of those things which are not a result of motion but come into being 
through mutation alone). This is evident in the case of substantial generation; for example, a 
child comes from its father and mother, who are its principles, and a fight from abusive 
language, which stirs the souls of men to quarrel. 

757. The second class in which this is made clear is that of human acts, whether ethical or 
political, in which that by whose will or intention others are moved or changed is called a 
principle. Thus those who hold civil, imperial, or even tyrannical power in states are said to 
have the principal places; for it is by their will that all things come to pass or are put into 
motion in states. Those men are said to have civil power who are put in command of 
particular offices in states, as judges and persons of this kind. Those are said to have imperial 
power who govern everyone without exception, as kings. And those hold tyrannical power 
who through violence and disregard for law keep royal power within their grip for their own 
benefit. 

758. He gives as the third class things made by art; for the arts too in a similar way are called 
principles of artificial things, because the motion necessary for producing an artifact begins 
from an art. And of these arts the architectonic, which "derive their name" from the word 
principle, i.e., those called principal arts, are said to be principles in the highest degree. For by 
architectonic arts we mean those which govern subordinate arts, as the art of the navigator 
governs the art of ship-building, and the military art governs the art of horsemanship. 

759. Again, in likeness to the order considered in external motions a certain order may also be 
observed in our apprehensions of things, and especially insofar as our act of understanding, 
by proceeding from principles to conclusions, bears a certain resemblance to motion. 
Therefore in another way that is said to be a principle from which a thing first becomes 
known; for example, we say that "postulates," i.e., axioms and assumptions, are principles of 
demonstrations. 

760. Causes are also said to be principles in these ways, "for all causes are principles." For 
the motion that terminates in a thing's being begins from some cause, although it is not 
designated a cause and a principle from the same point of view, as was pointed out above 
(750). 

761. Therefore, it is (404). 

Then he reduces all of the abovementioned senses of principle to one that is common. He says 
that all of the foregoing senses have something in common inasmuch as that is said to be a 
principle which comes first (1) either with reference to a thing's being (as the first part of a 
thing is said to be a principle) or (2) with reference to its coming to be (as the first mover is 
said to be a principle) or with reference to the knowing of it. 

762. But while all principles agree in the respect just mentioned, they nevertheless differ, 
because some are intrinsic and others extrinsic, as is clear from the above. Hence nature and 
element, which are intrinsic, can be principles-nature as that from which motion begins, and 
element as the first part in a thing's generation. "And mind," i.e., intellect, and "purpose," i.e., 
a man's intention, are said to be principles as extrinsic ones. Again, "a thing's substance," i.e., 
its form, which is its principle of being, is called an intrinsic principle, since a thing has being 


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by its form. Again, according to what has been said, that for the sake of which something 
comes to be is said to be one of its principles. For the good, which has the character of an end 
in the case of pursuing, and evil in that of shunning, are principles of the knowledge and 
motion of many things; that is, all those which are done for the sake of some end. For in the 
realm of nature, in that of moral acts, and in that of artifacts, demonstrations make special use 
of the final cause. 


LESSON 2 

The Four Classes of Causes. Several Causes of the Same Effect. Causes May Be Causes of 
Each Other. Contraries Have the Same Cause 

ARISTOTLE'S TEXT Chapter 2: 1013a 24-1013b 16 

405. In one sense the term cause means that from which, as something intrinsic, a thing 
comes to be, as the bronze of a statue and the silver of a goblet, and the genera of these. In 
another sense it means the form and pattern of a thing, i.e., the intelligible expression of the 
quiddity and its genera (for example, the ratio of 2: 1 and number in general are the cause of 
an octave chord) and the parts which are included in the intelligible expression. Again, that 
from which the first beginning of change or of rest comes is a cause; for example, an adviser 
is a cause, and a father is the cause of a child, and in general a maker is a cause of the thing 
made, and a changer a cause of the thing changed. Further, a thing is a cause inasmuch as it is 
an end, i.e., that for the sake of which something is done; for example, health is the cause of 
walking. For if we are asked why someone took a walk, we answer, "in order to be healthy"; 
and in saying this we think we have given the cause. And whatever occurs on the way to the 
end under the motion of something else is also a cause. For example, reducing, purging, drugs 
and instruments are causes of health; for all of these exist for the sake of the end, although 
they differ from each other inasmuch as some are instruments and others are processes. 
These, then, are nearly all the ways in which causes are spoken of. 

406. And since there are several senses in which causes are spoken of, it turns out that there 
are many causes of the same thing, and not in an accidental way. For example, both the maker 
of a statue and the bronze are causes of a statue not in any other respect but insofar as it is a 
statue. However, they are not causes in the same way, but the one as matter and the other as 
the source of motion. 

407. And there are things which are causes of each other. Pain, for example, is a cause of 
health, and health is a cause of pain, although not in the same way, but one as an end and the 
other as a source of motion. 

408. Further, the same thing is sometimes the cause of contraries; for that which when present 
is the cause of some particular thing, this when absent we sometimes blame for the contrary. 
Thus the cause of the loss of a ship is the absence of the pilot whose presence is the cause of 
the ship's safety. And both of these — the absence and the presence — are moving causes. 

COMMENTARY 

The four causes 


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763. Here the Philosopher distinguishes the various senses in which the term cause is used; 
and in regard to this he does two things. First, he enumerates the classes of causes. Second 
(783), he gives the modes of causes ("Now the modes"). 

In regard to the first part he does two things. First, he enumerates the various classes of 
causes. Second (777), he reduces them to four ("All the causes"). 

In regard to the first part he does two things. First, he enumerates the different classes of 
causes. Second (773), he clarifies certain things about the classes of causes ("And since"). 

He accordingly says, first, that in one sense the term cause means that from which a thing 
comes to be and is "something intrinsic," i.e., something which exists within the thing. This is 
said to distinguish it from a privation and also from a contrary; for a thing is said to come 
from a privation or from a contrary as from something which is not intrinsic; for example, 
white is said to come from black or from not-white. But a statue comes from bronze and a 
goblet from silver as from something which is intrinsic; for the nature bronze is not destroyed 
when a statue comes into being, nor is the nature silver destroyed when a goblet comes into 
being. Therefore the bronze of a statue and the silver of a goblet are causes in the sense of 
matter. He adds "and the genera of these," because if matter is the species of anything it is 
also its genus. For example, if the matter of a statue is bronze, its matter will also be metal, 
compound and body. The same holds true of other things. 

764. In another sense cause means the form and pattern of a thing, i.e., its exemplar. This is 
the formal cause, which is related to a thing in two ways. (1) In one way it stands as the 
intrinsic form of a thing, and in this respect it is called the formal principle of a thing. (2) In 
another way it stands as something which is extrinsic to a thing but is that in likeness to which 
it is made, and in this respect an exemplar is also called a thing's form. It is in this sense that 
Plato held the Ideas to be forms. Moreover, because it is from its form that each thing derives 
its nature, whether of its genus or of its species, and the nature of its genus or of its species is 
what is signified by the definition, which expresses its quiddity, the form of a thing is 
therefore the intelligible expression of its quiddity, i.e., the formula by which its quiddity is 
known. For even though certain material parts are given in the definition, still it is from a 
thing's form that the principal part of the definition comes. The reason why the form is a 
cause, then, is that it completes the intelligible expression of a thing's quiddity. And just as 
the genus of a particular matter is also matter, in a similar way the genera of forms are the 
forms of things; for example, the form of the octave chord is the ratio of 2:1. For when two 
notes stand to each other in the ratio of 2:1, the interval between them is one octave. Hence 
twoness is its form; for the ratio of 2:1 derives its meaning from twoness. And because 
number is the genus of twoness, we may therefore say in a general way that number is also 
the form of the octave, inasmuch as we may say that the octave chord involves the ratio of 
one number to another. And not only is the whole definition related to the thing defined as its 
form, but so also are the parts of the definition, i.e., those which are given directly in the 
definition. For just as two-footed animal capable of walking is the form of man, so also are 
animal, capable of walking and two-footed. But sometimes matter is given indirectly in the 
definition, as when the soul is said to be the actuality of a physical organic body having life 
potentially. 

765. In a third sense cause means that from which the first beginning of change or of rest 
comes, i.e., a moving or efficient cause. He says "of change or of rest," because motion and 
rest which are natural are traced back to the same cause, and the same is true of motion and of 
rest which are a result of force. For that cause by which something is moved to a place is the 


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same as that by which it is made to rest there. "An adviser" is an example of this kind of 
cause, for it is as a result of an adviser that motion begins in the one who acts upon his advice 
for the sake of safeguarding something. And in a similar way "a father is the cause of a 
child." In these two examples Aristotle touches upon the, two principles of motion from 
which all things come to be, namely, purpose in the case of an adviser, and nature in the case 
of a father. And in general every maker is a cause of the thing made and every changer a 
cause of the thing changed. 

766. Moreover, it should be noted that according to Avicenna, there are four modes of 
efficient cause, namely, perfective, dispositive, auxiliary and advisory. 

An efficient cause is said to be perfective inasmuch as it causes the final perfection of a thing, 
as the one who induces a substantial form in natural things or artificial forms in things made 
by art, as a builder induces the form of a house. 

767. An efficient cause is said to be dispositive if it does not induce the final form that 
perfects a thing but only prepares the matter for that form, as one who hews timbers and 
stones is said to build a house. This cause is not properly said to be the efficient cause of a 
house, because what he produces is only potentially a house. But he will be more properly an 
efficient cause if he induces the ultimate disposition on which the form necessarily follows; 
for example, man generates man without causing his intellect, which comes from an extrinsic 
cause. 

768. And an efficient cause is said to be auxiliary insofar as it contributes to the principal 
effect. Yet it differs from the principal efficient cause in that the principal efficient cause acts 
for its own end, whereas an auxiliary cause acts for an end which is not its own. For example, 
one who assists a king in war acts for the king's end. And this is the way in which a 
secondary cause is disposed for a primary cause. For in the case of all efficient causes which 
are directly subordinated to each other, a secondary cause acts because of the end of a 
primary cause; for example, the military art acts because of the end of the political art. 

769. And an advisory cause differs from a principal efficient cause inasmuch as it specifies 
the end and form of the activity. This is the way in which the first agent acting by intellect is 
related to every secondary agent, whether it be natural or intellectual. For in every case a first 
intellectual agent gives to a secondary agent its end and its form of activity; for example, the 
naval architect gives these to the shipwright, and the first intelligence does the same thing for 
everything in the natural world. 

770. Further, to this genus of cause is reduced everything that makes anything to be in any 
manner whatsoever, not only as regards substantial being, but also as regards accidental 
being, which occurs in every kind of motion. Hence he says not only that the maker is the 
cause of the thing made, but also that the changer is the cause of the thing changed. 

771. In a fourth sense cause means a thing's end, i.e., that for the sake of which something is 
done, as health is the cause of walking. And since it is less evident that the end is a cause in 
view of the fact that it comes into being last of all (which is also the reason why this cause 
was overlooked by the earlier philosophers, as was pointed out in Book I (1771), he therefore 
gives a special proof that an end is a cause. For to ask why or for what reason is to ask about a 
cause, because when we are asked why or for what reason someone walks, we reply properly 
by answering that he does so in order to be healthy. And when we answer in this way we 
think that we are stating the cause. Hence it is evident that the end is a cause. Moreover, not 


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only the ultimate reason for which an agent acts is said to be an end with respect to those 
things which precede it, but everything that is intermediate between the first agent and the 
ultimate end is also said to be an end with respect to the preceding agents. And similarly those 
things are said to be causes from which motion arises in subsequent things. For example, 
between the art of medicine, which is the first efficient cause in this order, and health, which 
is the ultimate end, there are these intermediates: reducing, which is the most proximate cause 
of health in those who have a superfluity of humors; purging, by means of which reducing is 
brought about; "drugs," i.e., laxative medicine, by means of which purging is accomplished; 
and "instruments," i.e., the instruments by which medicine or drugs are prepared and 
administered. And all such things exist for the sake of the end, although one of them is the 
end of another. For reducing is the end of purging, and purging is the end of purgatives. 
However, these intermediates differ from each other in that (1) some are instruments, i.e., the 
instruments by means of which medicine is prepared and administered (and the administered 
medicine itself is something which nature employs as an instrument); and (2) some — purging 
and reducing — are processes, i.e., operations or activities. 

772. He concludes, then, that "these are the ways in which causes are spoken of (405)," i.e., 
the four ways; and he adds "nearly all" because of the modes of causes which he gives below. 
Or he also adds this because the same classes of causes are not found for the same reason in 
all things. 

773. And since (406). 

Then he indicates certain points which follow from the things said above about the causes, 
and there are four of these. The first is that, since the term cause is used in many senses, there 
may be several causes of one thing not accidentally but properly. For the fact that there are 
many causes of one thing accidentally presents no difficulty, because many things may be 
accidents of something that is the proper cause of some effect, and all of these can be said to 
be accidental causes of that effect. But that there are several proper causes of one thing 
becomes evident from the fact that causes are spoken of in various ways. For the maker of a 
statue is a proper cause and not an accidental cause of a statue, and so also is the bronze, but 
not in the same way. For it is impossible that there should be many proper causes of the same 
thing within the same genus and in the same order, although there can be many causes 
providing that (1) one is proximate and another remote; or (2) that neither of them is of itself 
a sufficient cause, but both together. An example would be many men rowing a boat. Now in 
the case in point these two things are causes of a statue in different ways: the bronze as 
matter, and the artist as efficient cause. 

774. And there are (407). 

Then he sets down the second fact that may be drawn from the foregoing discussion. He says 
that it may also happen that any two things may be the cause of each other, although this is 
impossible in the same class of cause. But it is evident that this may happen when causes are 
spoken of in different senses. For example, the pain resulting from a wound is a cause of 
health as an efficient cause or source of motion, whereas health is the cause of pain as an end. 
For it is impossible, that a thing should be both a cause and something caused. Another text 
states this better, saying that "exercise is the cause of physical fitness," i.e., of the good 
disposition caused by moderate exercise, which promotes digestion and uses up superfluous 
humors. 

775. Now it must be borne in mind that, although four causes are given above, two of these 
are related to one another, and so also are the other two. (1) The efficient cause is related to 


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the final cause, and (2) the material cause is related to the formal cause. The efficient cause is 
related to the final cause because the efficient cause is the starting point of motion and the 
final cause is its terminus. There is a similar relationship between matter and form. For form 
gives being, and matter receives it. Hence the efficient cause is the cause of the final cause, 
and the final cause is the cause of the efficient cause. The efficient cause is the cause of the 
final cause inasmuch as it makes the final cause be, because by causing motion the efficient 
cause brings about the final cause. But the final cause is the cause of the efficient cause, not in 
the sense that it makes it be, but inasmuch as it is the reason for the causality of the efficient 
cause. For an efficient cause is a cause inasmuch as it acts, and it acts only because of the 
final cause. Hence the efficient cause derives its causality from the final cause. And form and 
matter are mutual causes of being: form is a cause of matter inasmuch as it gives actual being 
to matter, and matter is a cause of form inasmuch as it supports form in being. And I say that 
both of these together are causes of being either in an unqualified sense or with some 
qualification. For substantial form gives being absolutely to matter, whereas accidental form, 
inasmuch as it is a form, gives being in a qualified sense. And matter sometimes does not 
support a form in being in an unqualified sense but according as it is the form of this 
particular thing and has being in this particular thing. This is what happens in the case of the 
human body in relation to the rational soul. 

776. Further, the same thing (408). 

Then he gives the third conclusion that may be drawn from the foregoing discussion. He says 
that the same thing can be the cause of contraries. This would also seem to be difficult or 
impossible if it were related to both in the same way. But it is the cause of each in a different 
way. For that which when present is the cause of some particular thing, this when absent "we 
blame," i.e., we hold it responsible, "for the contrary." For example, it is evident that by his 
presence the pilot is the cause of a ship's safety, and we say that his absence is the cause of 
the ship's loss. And lest someone might think that this is to be attributed to different classes of 
causes, just as the preceding two were, he therefore adds that both of these may be reduced to 
the same class of cause — the moving cause. For the opposite of a cause is the cause of an 
opposite effect in the same line of causality as that in which the original cause was the cause 
of its effect. 


LESSON 3 

All Causes Reduced to Four Classes 
ARISTOTLE'S TEXT Chapter 2: 1013b 16-1014a 25 

409. All the causes mentioned fall under one of the four classes which are most evident. For 
the elements of syllables, the matter of things made by art, fire and earth and all such 
elements of bodies, the parts of a whole, and the premises of a conclusion, are all causes in 
the sense of that from which things are made. But of these some are causes as a subject, for 
example, parts, and others as the essence, for example, the whole, the composition and the 
species, whereas the seed, the physician, the adviser, and in general every agent, are all 
sources of change or of rest. But the others are causes as the end and the good of other things. 
For that for the sake of which other things come to be is the greatest good and the end of other 
things. And it makes no difference whether we say that it is a good or an apparent good. 


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These, then, are the causes, and this the number of their classes. 

410. Now the modes of causes are many in number, but these become fewer when 
summarized. For causes are spoken of in many senses; and of those which belong to the same 
class, some are prior and some subsequent. For example, both the physician and one 
possessing an art are causes of health, and both the ratio of 2:1 and number are causes of the 
octave chord; and always those classes which contain singulars. Further, a thing may be a 
cause in the sense of an accident, and the classes which contain these; for example, in one 
sense the cause of a statue is Polyclitus and in another a sculptor, because it is accidental that 
a sculptor should be Polyclitus. And the universals which contain accidents are causes; for 
example, man is the cause of a statue, and even generally animal, because Polyclitus is a man 
and an animal. And of accidental causes some are more remote and some more proximate 
than others. Thus what is white and what is musical might be said to be the causes of a statue, 
and not just Polyclitus or man. Again, in addition to all of these, i.e., both proper causes and 
accidental causes, some are said to be causes potentially and some actually, as a builder and 
one who is building. And the distinctions which have been made will apply in like manner to 
the effects of these causes, for example, to this statue, or to a statue, or to an image generally, 
or to this bronze, or to bronze, or to matter in general. And the same applies to accidental 
effects. Again, both proper and accidental causes may be spoken of together, so that the cause 
of a statue may be referred to as neither Polyclitus nor a sculptor but the sculptor Polyclitus. 
But while all these varieties of causes are six in number, each is spoken of in two ways; for 
causes are either singular or generic; either proper or accidental, or generically accidental; or 
they are spoken of in combination or singly; and again they are either active or potential 
causes. But they differ in this respect, that active causes, i.e. singular causes, exist or cease to 
exist simultaneously with their effects, as this particular one who is healing with this 
particular person who is being healed, and as this particular builder with this particular thing 
which is being built. But this is not always true of potential causes; for the builder and the 
thing built do not cease to exist at the same time. 

COMMENTARY 

Four modes of causes 

111. Here the philosopher reduces all causes to the classes of causes mentioned above (409), 
saying that all those things which are called causes fall into one of the four classes mentioned 
above. For "elements," i.e., letters, are said to be the causes of syllables; and the matter of 
artificial things is said to be their cause; and fire and earth and all simple bodies of this kind 
are said to be the causes of compounds. And parts are said to be the causes of a whole, and 
"premises," i.e., propositions previously set down from which conclusions are drawn, are said 
to be the causes of the conclusion. And in all of these cases cause has a single formal aspect 
according as cause means that from which a thing is produced, and this is the formal aspect of 
material cause. 

778. Now it must be noted that propositions are said to constitute the matter of a conclusion, 
not inasmuch as they exist under such a form, or according to their force (for in this way they 
would rather have the formal aspect of an efficient cause), but with reference to the terms of 
which they are composed. For a conclusion is constituted of the terms contained in the 
premises, i.e., of the major and minor terms. 

779. And of those things of which something is composed, some are like a subject, for 
example, parts and the other things mentioned above, whereas some are like the essence, for 


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example, the whole, the composition and the species, which have the character of a form 
whereby a thing's essence is made complete. For it must be borne in mind that (1) sometimes 
one thing is the matter of something else in an unqualified sense (for example, silver of a 
goblet), and then the form corresponding to such a matter can be called the species. (2) But 
sometimes many things taken together constitute the matter of a thing; and this may occur in 
three ways, (a) For sometimes things are united merely by their arrangement, as the men in an 
army or the houses in a city; and then the whole has the role of a form which is designated by 
the term army or city, (b) And sometimes things are united not just by arrangement alone but 
by contact and a bond, as is evident in the parts of a house; and then their composition has the 
role of a form, (c) And sometimes the alteration of the component parts is added to the above, 
as occurs in the case of a compound; and then the compound state itself is the form, and this 
is still a kind of composition. And a thing's essence is derived from any one of these 
three — the composition' species, or whole — as becomes clear when an army, a house, or a 
goblet is defined. Thus we have two classes of cause. 

780. But the seed, the physician and the adviser, and in general every agent, are called causes 
for a different reason, namely, because they are the sources of motion and rest. Hence this is 
now a different class of cause because of a different formal aspect of causality. He puts seed 
in this class of cause because he is of the opinion that the seed has active power, whereas a 
woman' s menstrual fluid has the role of the matter of the offspring. 

78 1 . There is a fourth formal aspect of causality inasmuch as some things are said to be 
causes in the sense of the end and good of other things. For that for the sake of which 
something else comes to be is the greatest good "and the end" of other things, i.e., it is 
naturally disposed to be their end. But because someone could raise the objection that an end 
is not always a good since certain agents sometimes inordinately set up an evil as their end, he 
therefore replies that it makes no difference to his thesis whether we speak of what is good 
without qualification or of an apparent good. For one who acts does so, properly speaking, 
because of a good, for this is what he has in mind. And one acts for the sake of an evil 
accidentally inasmuch as he happens to think that it is good. For no one acts for the sake of 
something with evil in view. 

782. Moreover, it must be noted that, even though the end is the last thing to come into being 
in some cases, it is always prior in causality. Hence it is called the "cause of causes", because 
it is the cause of the causality of all causes. For it is the cause of efficient causality, as has 
already been pointed out (775); and the efficient cause is the cause of the causality of both the 
matter and the form, because by its motion it causes matter to be receptive of form and makes 
form exist in matter. Therefore the final cause is also the cause of the causality of both the 
matter and the form. Hence in those cases in which something is done for an end (as occurs in 
the realm of natural things, in that of moral matters, and in that of art), the most forceful 
demonstrations are derived from the final cause. Therefore he concludes that the foregoing 
are causes, and that causes are distinguished into this number of classes. 

783. Now the modes (410). 

Then he distinguishes between the modes of causes. And causes are distinguished into classes 
and into modes. For the division of causes into classes is based on different formal aspects of 
causality, and is therefore equivalently a division based on essential differences, which 
constitute species. But the division of causes into modes is based on the different 
relationships between causes and things caused, and therefore pertains to those causes which 
have the same formal aspect of causality. An example of this is the division of causes into 


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proper and accidental causes, and into remote and proximate causes. Therefore this division is 
equivalently a division based on accidental differences, which do not constitute different 
species. 

784. He accordingly says that there are many modes of causes, but that these are found to be 
fewer in number when "summarized," i.e., when brought together under one head. For even 
though proper causes and accidental causes are two modes, they are still reduced to one head 
insofar as both may be considered from the same point of view. The same thing is true of the 
other different modes. For many different modes of causes are spoken of, not only with 
reference to the different species of causes, but also with reference to causes of the same 
species, namely, those which are reduced to one class of cause. 

785. (1) For one cause is said to be prior and another subsequent; and causes are prior or 
subsequent in two ways: (1) In one way, when there are many distinct causes which are 
related to each other, one of which is primary and remote, and another secondary and 
proximate (as in the case of efficient causes man generates man as a proximate and 
subsequent cause, but the sun as a prior and remote cause); and the same thing can be 
considered in the case of the other classes of causes. (2) In another way, when the cause is 
numerically one and the same, but is considered according to the sequence which reason sets 
up between the universal and the particular; for the universal is naturally prior and the 
particular subsequent. 

786. But he omits the first way and considers the second. For in the second way the effect is 
the immediate result of both causes, i.e., of both the prior and subsequent cause; but this 
cannot happen in the first way. Hence he says that the cause of health is both the physician 
and one possessing an art, who belong to the class of efficient cause: one possessing an art as 
a universal and prior cause, and the physician as a particular, or special, and subsequent 
cause. The same thing is true of the formal cause, since this cause may also be considered in 
two ways; for example, for an octave chord "double," or the ratio of 2:1, or the number two, 
is a formal cause as one that is special and subsequent, whereas number, or the ratio of one 
number to another or to the unit, is like a universal and prior cause. And in this way too 
"always those classes which contain singulars," i.e., universals, are said to be prior causes. 

787. (2) Causes are distinguished in another way inasmuch as one thing is said to be a proper 
cause and another an accidental cause. For just as proper causes are divided into universal and 
particular, or into prior and subsequent, so also are accidental causes. Therefore, not only 
accidental causes themselves are called such, but so also are the classes which contain these. 
For example, a sculptor is the proper cause of a statue, and Polyclitus is an accidental cause 
inasmuch as he happens to be a sculptor. And just as Polyclitus is an accidental cause of a 
statue, in a similar way all universals "which contain accidents," i.e., accidental causes, are 
said to be accidental causes, for example, man and animal, which contain under themselves 
Polyclitus, who is a man and an animal. 

788. And just as some proper causes are proximate and some remote, as was pointed out 
above, so also is this the case with accidental causes. For Polyclitus is a more proximate cause 
of a statue than what is white or what is musical. For an accidental mode of predication is 
more remote when an accident is predicated of an accident than when an accident is 
predicated of a subject. For one accident is predicated of another only because both are 
predicated of a subject. Hence when something pertaining to one accident is predicated of 
another, as when something pertaining to a builder is predicated of a musician, this mode of 
predication is more remote than one in which something is predicated of the subject of an 


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accident, as when something pertaining to a builder is predicated of Polyclitus. 

789. Now it must be borne in mind that one thing can be said to be the accidental cause of 
something else in two ways: (1) in one way, from the viewpoint of the cause; because 
whatever is accidental to a cause is itself called an accidental cause, for example, when we 
say that something white is the cause of a house. (2) In another way, from the viewpoint of 
the effect, i.e., inasmuch as one thing is said to be an accidental cause of something else 
because it is accidental to the proper effect. This can happen in three ways: 

The first is that the thing has a necessary connection with the effect. Thus that which removes 
an obstacle is said to be a mover accidentally. This is the case whether that accident is a 
contrary, as when bile prevents coolness (and thus scammony is said to produce coolness 
accidentally, not because it causes coolness, but because it removes the obstacle preventing 
coolness, i.e., bile, which is its contrary); or even if it is not a contrary, as when a pillar 
hinders the movement of a stone which rests upon it, so that one who removes the pillar is 
said to move the stone accidentally. 

In a second way, something is accidental to the proper effect when the accident is connected 
with the effect neither necessarily nor in the majority of cases but seldom, as the discovery of 
a treasure is connected with digging in the soil. It is in this way that fortune and chance are 
said to be accidental causes. 

In a third way things are accidental to the effect when they have no connection except perhaps 
in the mind, as when someone says that he is the cause of an earthquake because an 
earthquake took place when he entered the house. 

790. [Cross-division of all] And besides the distinction of all things into causes in themselves 
or proper causes and accidental causes, there is a third division of causes inasmuch as some 
things are causes potentially and some actually, i.e., actively. For example, the cause of 
building is a builder in a state of potency (for this designates his habit or office), or one who 
is actually building. 

791. And the same distinctions which apply to causes can apply to the effects of which these 
causes are the causes. For effects, whether particular or universal, can be divided into prior 
and subsequent, as a sculptor may be called the cause of this statue, which is subsequent; or 
of a statue, which is more universal and prior; or of an image, which is still more universal. 
And similarly something is the formal cause of this particular bronze; or of bronze, which is 
more universal; or of matter, which is still more universal. The same things can be said of 
accidental effects, i.e., of things produced by accident. For a sculptor who is the cause of a 
statue is also the cause of the heaviness, whiteness or redness which are in it as accidents 
from the matter and are not caused by this agent. 

792. (3) Again, he gives a fourth division of causes, namely, the division into simple causes 
and composite causes. A cause is said to be simple (a) when, for example, in the case of a 
statue, the proper cause alone is considered, as a sculptor, or when an accidental cause alone 
is considered, as Polyclitus. But a cause is said to be composite when both are taken together, 
for example, when we say that the cause of a statue is the sculptor Polyclitus. 

793. (b) There is moreover another way in which causes are said to be composite, i.e., when 
several causes act together to produce one effect, for example, when many men act together 
in order to row a boat, or when many stones combine in order to constitute the matter of a 


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house. But he omits the latter way because no one of these things taken in itself is the cause, 
but a part of the cause. 

794. And having given these different modes of causes, he brings out their number, saying 
that these modes of causes are six in number, and that each of these have two alternatives so 
that twelve result. For these six modes are (1-2) either singular or generic (or, as he called 
them above, prior and subsequent); (3-4) either proper or accidental (to which the genus of 
the accident is also reduced, for the genus to which an accident belongs is an accidental 
cause); and again, (5-6) either composite or simple. Now these six modes are further divided 
by potency and actuality and thus are twelve in number. Now the reason why all these modes 
must be divided by potency and actuality is that potency and actuality distinguish the 
connection between cause and effect. For active causes are at one and the same time 
particulars and cease to exist along with their effects; for example, this act of healing ceases 
with this act of recovering health, and this act of building with this thing being built; for a 
thing cannot be actually being built unless something is actually building. But potential 
causes do not always cease to exist when their effects cease; for example, a house and a 
builder do not cease to exist at one and the same time. In some cases, however, it does happen 
that when the activity of the efficient cause ceases the substance of the effect ceases. This 
occurs in the case of those things whose being consists in coming to be, or whose cause is not 
only the cause of their coming to be but also of their being. For example, when the sun' s 
illumination is removed from the atmosphere, light ceases to be. He says "singular causes" 
because acts belong to singular things, as was stated in Book I of this work (21). 


LESSON 4 

The Proper Meaning of Element; Elements in Words, Natural Bodies, and Demonstrations. 
Transferred Usages of "Element" and Their Common Basis 

ARISTOTLE'S TEXT Chapter 3: 1014a 25-1014b 15 

41 1. The inherent principle of which a thing is first composed and which is not divisible into 
another species is called an element. For example, the elements of a word are the parts of 
which a word is composed and into which it is ultimately divided and which are not further 
divided into other words specifically different from them. But if they are divided, their parts 
are alike, as the parts of water are water; but this is not true of the syllable. Similarly, people 
who speak of the elements of bodies mean the component parts into which bodies are 
ultimately divided and which are not divided into other bodies specifically different. And 
whether such parts are one or many, they call them elements. And similarly the parts of 
diagrams are called elements, and in general the parts of demonstrations; for the primary 
demonstrations which are contained in many other demonstrations are called the elements of 
demonstrations; and such are the primary syllogisms which are composed of three terms and 
proceed through one middle term. 

412. People also use the term element in a transferred sense of anything which is one and 
small and useful for many purposes; and for this reason anything which is small and simple 
and indivisible is called an element. Hence it follows that the most universal things are 
elements, because each of them, being one and simple, is found in many things, either in all 
or in most of them. And to some the unit and the point seem to be principles. Therefore, since 


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what are called genera are universal and indivisible (for their formal character is one), some 
men call the genera elements, and these more than a difference, since a genus is more 
universal. For where the difference is present the genus also follows, but the difference is not 
always present where the genus is. And in all these cases it is common for the element of each 
thing to be the primary component of each thing. 

COMMENTARY 

Element 

795. Here he distinguishes the different senses of the term element, and in regard to this lie 
does two things. First, he gives the different senses in which the term element is used. Second 
(807), he indicates what all of them have in common ("And in all these"). 

In regard to the first he does two things. First, he explains how the term element is used in its 
proper sense; and second (802), how it is used in transferred senses ("People also use"). 

First, he gives a sort of description of an element, and from this one can gather the four notes 
contained in its definition. The first is that an element is a cause in the sense of that from 
which a thing comes to be; and from this it is clear that an element is placed in the class of 
material cause. 

796. The second is that an element is the principle from which something first comes to be. 
For copper is that from which a statue comes to be, but it is still not an element because it has 
some matter from which it comes to be. 

797. The third is that an element is inherent or intrinsic; and for this reason, it differs from 
everything of a transitory nature from which a thing comes to be, whether it be a privation or 
a contrary or the matter subject to contrariety and privation, which is transitory; for example, 
when we say that a musical man comes from a nonmusical man, or that the musical comes 
from the non-musical. For elements must remain in the things of which they are the elements. 

798. The fourth is that an element has a species which is not divisible into different species; 
and thus an element differs from first matter, which has no species, and also from every sort 
of matter which is capable of being divided into different species, as blood and things of this 
kind. 

Hence he says, as the first note, that an element is that of which a thing is composed; as the 
second, that it is that of which a thing is "first" composed; as the third, that it is "an inherent 
principle"; and as the fourth, that it is "not divisible into another species." 

799. He illustrates this definition of element in four cases in which we use the term element. 
For we say that letters are the elements of a word because every word is composed of them, 
and of them primarily. This is evident from the fact that all words are divided into letters as 
ultimate things; for what is last in the process of dissolution must be first in the process of 
composition. But letters are not further divided into other words which are specifically 
different. Yet if they should be divided in any way, the parts in which the division results 
would be "alike," i.e., specifically the same, just as all parts of water are water. Now letters 
are divided according to the amount of time required to pronounce them, inasmuch as a long 
letter is said to require two periods of time, and a short letter one. But while the parts into 
which letters are so divided do not differ as the species of words do, this is not the case with a 


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syllable; for its parts are specifically different, since the sounds which a vowel and a 
consonant make, of which a syllable is composed, are specifically different. 

800. He gives as a second example natural bodies, certain of which we also call the elements 
of certain others. For those things into which all compounds are ultimately dissolved are 
called their elements; and therefore they are the things of which bodies of this kind are 
composed. But those bodies which are called elements are not divisible into other bodies 
which are specifically different, but into like parts, as any part of water is water. And all those 
who held for one such body into which every body is dissolved and which is itself incapable 
of being further divided , said that there is one element. Some said that it is water, some air, 
and some fire. But those who posited many such bodies also said there are many elements. 
Now it should be borne in mind that when it is set down in the definition of an element that an 
element is not divisible into different species, this should not be understood of the parts into 
which a thing is divided in a quantitative division (for wood would then be an element, since 
any part of wood is wood), but in a division made by alteration, as compounds are dissolved 
into simple bodies. 

801. As a third example he gives the order of demonstrations, in which we also employ the 
word element; for example, we speak of Euclid's Book of Elements. And he says that, in a 
way similar and close to those mentioned, those things which "are parts of diagrams," i.e., the 
constituents of geometrical figures, are called elements. This can be said not only of the 
demonstrations in geometry but universally of all demonstrations. For those demonstrations 
which have only three terms are called the elements of other demonstrations, because the 
others are composed of them and resolved into them. This is shown as follows: a second 
demonstration takes as its starting point the conclusion of a first demonstration, whose terms 
are understood to contain the middle term which was the starting point of the first 
demonstration. Thus the second demonstration will proceed from four terms the first from 
three only, the third from five, and the fourth from six; so that each demonstration adds one 
term. Thus it is clear that first demonstrations are included in subsequent ones, as when this 
first demonstration — every B is A, every C is B, therefore every C is A — is included in this 
demonstration — every C is A, every D is C, therefore every D is A; and this again is included 
in the demonstration whose conclusion is that every E is A, so that for this final conclusion 
there seems to be one syllogism composed of several syllogisms having several middle terms. 
This may be expressed thus: every B is A, every C is B, every D is C, every E is D, therefore 
every E is A. Hence a first demonstration, which has one middle term and only three terms, is 
simple and not reducible to another demonstration, whereas all other demonstrations are 
reducible to it. Hence first syllogisms, which come from three terms by way of one middle 
term, are called elements. 

802. People also use (412). 

Here he shows how the term element is used in a transferred sense. He says that some men, 
on the basis of the foregoing notion or meaning of element, have used the term in a 
transferred sense to signify anything that is one and small and useful for many purposes. For 
from the fact that an element is indivisible they understood that it is one; and from the fact 
that it is first they understood that it is simple; and from the fact that other things are 
composed of elements they understood that an element is useful for many purposes. Hence 
they set up this definition of an element in order that they might say that everything which is 
smallest in quantity and simple (inasmuch as it is not composed of other things) and incapable 
of division into different species, is an element. 


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803. But when they had set up this definition of element, it turned out that by using it in a 
transferred sense they had invented two senses of element. First, they called the most 
universal things elements; for a universal is one in definition and is simple (because its 
definition is not composed of different parts) and is found in many things, and thus is useful 
for many purposes, whether it be found in all things, as unity and being are, or in most things, 
as the other genera. And by the same reasoning it came about, second, that they called points 
and units principles or elements because each of them is one simple thing and useful for many 
purposes. 

804. But in this respect they fell short of the true notion of a principle, because universals are 
not the matter of which particular things are composed but predicate their very substance. 
And similarly points are not the matter of a line, for a line is not composed of points. 

805. Now with this transferred notion of element established, the solution to a question 
disputed in Book III (431-36) becomes clear, i.e., whether a genus or a species is more an 
element, and whether a genus or a difference is more an element; for it clearly follows that 
genera are elements to a greater degree because genera are more universal and indivisible. For 
there is no concept or definition of them which must be composed of genera and differences, 
but it is species which are properly defined. And if a genus is defined, it is not defined insofar 
as it is a genus but insofar as it is a species. Hence a species is divided into different parts and 
thus does not have the character of an element. But a genus is not divisible into different 
parts, and therefore they said that genera are elements more than species. Another translation 
reads, "For their formal character is one," that is, indivisible, because even though genera do 
not have a definition, still what is signified by the term genus is a simple conception of the 
intellect which can be called a definition. 

806. And just as a genus is more an element than a species is because it is simpler, in a similar 
way it is more an element than a difference is, even though a difference is simple, because a 
genus is more universal. This is clear from the fact that anything which has a difference has a 
genus, since essential differences do not transcend a genus; but not everything which has a 
genus necessarily has a difference. 

807. Last of all he says that all of the foregoing senses of element have this note in common, 
that an element is the primary component of each being, as has been stated. 


LESSON 5 

Five Senses of the Term Nature 

ARISTOTLE'S TEXT Chapter 4: 1014b 15- 1015a 20 

413. Nature means, in one sense, the generation of things that are born, as if one were to 
pronounce the letter u [in fusij] long. And in another sense it means the immanent principle 
from which anything generated is first produced. Again, it means the source of the primary 
motion in any beings which are by nature, and it is in each inasmuch as it is such. Now all 
those things are said to be born which increase through something else by touching and by 
existing together, or by being naturally joined, as in the case of embryos. But being born 
together differs from touching, for in the latter case there need be nothing but contact. But in 


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things which are naturally joined together there is some one same thing in both, instead of 
contact, which causes them to be one, and which makes them to be one in quantity and 
continuity but not in quality. Again, nature means the primary thing of which a natural being 
is composed or from which it comes to be, when it is unformed and immutable by its own 
power; for example, the bronze of a statue or of bronze articles is said to be their nature, and 
the wood of wooden things, and the same applies in the case of other things. For each thing 
comes from these though its primary matter is preserved. For it is also in this sense that men 
speak of the elements of natural beings as their nature; some calling it fire, others earth, others 
water, others air, and others something similar to these, whereas others call all of them nature. 
In still another sense nature means the substance of things which are by nature, as those who 
say that nature is the primary composition of a thing, as Empedocles says, "Of nothing that 
exists is there nature, but only the mixing and separating-out of what has been mixed. Nature 
is but the name men give to these. For this reason we do not say that things which are or come 
to be by nature have a nature, even when that from which they can be or come to be is already 
present, so long as they do not have their form or species. Hence that which is composed of 
both of these exists by nature, as animals and their parts. 

414. Again, nature is the primary matter of a thing, and this in two senses: either what is 
primary with respect to this particular thing, or primary in general; for example, the primary 
matter of bronze articles is bronze, but in general it is perhaps water, if everything capable of 
being liquefied is water. And nature is also a thing's form or substance, i.e., the terminus of 
the process of generation. But metaphorically speaking every substance in general is called 
nature because of form or species, for the nature of a thing is also a kind of substance. 

415. Hence, from what has been said, in its primary and proper sense nature is the substance 
of those things which have within themselves as such the source of their motion. For matter is 
called nature because it is receptive of this. And processes of generation and growth are called 
nature because they are motions proceeding from it. And nature is the source of motion in 
those things which are by nature, and it is something present in them either potentially or in 
complete actuality. 

COMMENTARY 

Nature 

808. Here he gives the different meanings of the term nature. And even though an 
investigation of the term nature appears not to belong to first philosophy but rather to the 
philosophy of nature, he nevertheless gives the different meanings of this term here, because 
according to one of its common meanings nature is predicated of every substance, as he will 
make clear. Hence it falls under the consideration of first philosophy just as universal 
substance does. 

In regard to the first he does two things. First (808), he distinguishes the different senses in 
which the term nature is used. Second (824), he reduces all of these to one primary notion 
("Hence, from what"). 

In regard to the first he does two things. First, he gives five principal senses in which the 
term, nature is used. Second (821), he gives two additional senses connected with the last two 
of these ("Again, nature"). 


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(1) He accordingly says, first, that in one sense nature means the process of generation of 
things that are generated, or, according to another text which states this in a better way, "of 
things that are born." For not everything that is generated can be said to be born but only 
living things, for example, plants and animals and their parts. The generation of non-living 
things cannot be called nature, properly speaking, according to the common use of the term, 
but only the generation of living things inasmuch as nature may mean the nativity or birth of a 
thing... Yet even from this text it can be understood that the term nature means the generation 
of living things by a certain lengthening or extension of usage. 

809. Again, from the fact that nature was first used to designate the birth of a thing there 
followed a second use of the term, so that nature came to mean the principle of generation 
from which a thing comes to be, or that from which as from an intrinsic principle something 
born is first generated. 

810. And as a result of the likeness between birth and other kinds of motion the meaning of 
the term nature has been extended farther, so that in a third sense it means the source from 
which motion begins in any being according to its nature, provided that it is present in it 
insofar as it is such a being and not accidentally. For example, the principle of health, which 
is the medical art, is not present in a physician who is ill insofar as he is ill but insofar as he is 
a physician. And he is not healed insofar as he is a physician but insofar as he is ill; and thus 
the source of motion is not in him insofar as he is moved. This is the definition of nature 
given in Book II of the Physics. 

811. And because he mentioned things that are born, he also shows what it means in the 
proper sense "to be born," as another text says, and in place of which this text incorrectly says 
"to be generated." For the generation of living things differs from that of non-living things, 
because a non-living thing is not generated by being joined or united to its generator, as fire is 
generated by fire and water by water. But the generation of a living thing comes about 
through some kind of union with the principle of generation. And because the addition of 
quantity to quantity causes increase, therefore in the generation of living things there seems to 
be a certain increase, as when a tree puts forth foliage and fruit. Hence he says that those 
things are said to be born which "increase," i.e., have some increase together with the 
principle of generation [i.e. multiply]. 

812. But this kind of increase differs from that class of motion which is called increase [or 
augmentation], by which things that are already born are moved or changed. For a thing that 
increases within itself does so because the part added passes over into the substance of that 
thing, as food passes over into the substance of the one nourished. But anything that is born is 
added to the thing from which it is born as something other and different, and not as 
something that passes over into its substance. Hence he says that it increases "through 
something distinct" or something else, as if to say that this increase comes about through the 
addition of something that is other or different. 

813. But addition that brings about increase can be understood to take place in two ways: in 
one way, "by touching," i.e., by contact alone; in another way, "by existing together," i.e., by 
the fact that two things are produced together and naturally connected with each other, as the 
arms and sinews; "and by being joined," i.e., by the fact that something is naturally adapted to 
something else already existing, as hair to the head and teeth to the gums. In place of this 
another text reads, more appropriately, "by being born together with," and "by being 
connected with at birth." Now in the generation of living things addition comes about not 
only by contact but also by a kind of joining together or natural connection, as is evident in 


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the case of embryos, which are not only in contact in the womb, but are also bound to it at the 
beginning of their gene